diff --git a/apps/web/src/components/ComposerPromptEditorTiptap.input.browser.test.tsx b/apps/web/src/components/ComposerPromptEditorTiptap.input.browser.test.tsx
index 925319680d40d..5bbe94d4a909d 100644
--- a/apps/web/src/components/ComposerPromptEditorTiptap.input.browser.test.tsx
+++ b/apps/web/src/components/ComposerPromptEditorTiptap.input.browser.test.tsx
@@ -321,6 +321,64 @@ it("keeps unknown dollar names editable when restoring and pasting a draft", asy
   expect(serializeEditorDoc(editor.state.doc).value).toBe(value);
 });
 
+it("pastes arithmetic stars verbatim and still styles pasted markdown", async () => {
+  await using screen = await mountEditor("", true, []);
+  const { editor } = screen;
+  const paste = async (text: string) => {
+    await act(async () => {
+      editor.commands.selectAll();
+      const clipboardData = new DataTransfer();
+      clipboardData.setData("text/plain", text);
+      editor.view.dom.dispatchEvent(
+        new ClipboardEvent("paste", { clipboardData, cancelable: true }),
+      );
+    });
+  };
+  const code = "signal = (7 * 2**3 * 5)**4";
+  await paste(code);
+  expect(serializeEditorDoc(editor.state.doc).value).toBe(code);
+  await paste("a **bold** and *soft* word");
+  expect(serializeEditorDoc(editor.state.doc).value).toBe("a **bold** and *soft* word");
+  expect(editor.state.doc.textContent).toBe("a bold and soft word");
+});
+
+it("parses markdown dropped from outside, keeps dropped arithmetic verbatim, and focuses", async () => {
+  await using screen = await mountEditor("", true, []);
+  const { editor } = screen;
+  const drop = async (text: string, html?: string) => {
+    await act(async () => {
+      editor.commands.clearContent();
+      editor.view.dom.blur();
+      const dataTransfer = new DataTransfer();
+      dataTransfer.setData("text/plain", text);
+      if (html) dataTransfer.setData("text/html", html);
+      const { left, top } = editor.view.coordsAtPos(1);
+      editor.view.dom.dispatchEvent(
+        new DragEvent("drop", {
+          dataTransfer,
+          clientX: left,
+          clientY: top + 1,
+          bubbles: true,
+          cancelable: true,
+        }),
+      );
+    });
+  };
+  await drop("a **bold** and *soft* word");
+  expect(serializeEditorDoc(editor.state.doc).value).toBe("a **bold** and *soft* word");
+  expect(editor.state.doc.textContent).toBe("a bold and soft word");
+  expect(editor.view.hasFocus()).toBe(true);
+  await drop("bold", "<p><strong>bold</strong></p>");
+  expect(serializeEditorDoc(editor.state.doc).value).toBe("**bold**");
+  const code = "signal = (7 * 2**3 * 5)**4";
+  await drop(code);
+  expect(serializeEditorDoc(editor.state.doc).value).toBe(code);
+  // A drag that started inside the editor is ProseMirror's move, not an external text drop.
+  editor.view.dragging = { slice: editor.state.doc.slice(0, 0), move: false };
+  await drop("a **bold** word");
+  expect(serializeEditorDoc(editor.state.doc).value).toBe("");
+});
+
 it("keeps the caret inside unknown dollar text across rich and plain remounts", async () => {
   const value = "echo $HOME now";
   await using screen = await mountEditor(value);
diff --git a/apps/web/src/components/ComposerPromptEditorTiptap.tsx b/apps/web/src/components/ComposerPromptEditorTiptap.tsx
index 1986cc888efba..fa409fdf6ab70 100644
--- a/apps/web/src/components/ComposerPromptEditorTiptap.tsx
+++ b/apps/web/src/components/ComposerPromptEditorTiptap.tsx
@@ -1098,6 +1098,101 @@ function ComposerPromptEditorTiptapInner(
     "aria-placeholder": placeholder,
   };
 
+  const insertClipboardText = (view: EditorView, clipboardData: DataTransfer): boolean => {
+    const pastedText = clipboardData.getData("text/plain");
+    if (!pastedText) return false;
+    // Paste verbatim inside fences; markdown parsing would split blocks and create unsupported chips.
+    if (isInCodeBlock(view)) {
+      const { from, to } = view.state.selection;
+      view.dispatch(
+        markAsClipboardEdit(
+          view.state.tr.insertText(pastedText, from, to),
+          "paste",
+        ).scrollIntoView(),
+      );
+      return true;
+    }
+    // Shown Markdown source is parsed when the caret leaves, so paste one line into it as text.
+    const sourceType = view.state.schema.marks[MARKDOWN_SOURCE_MARK];
+    const { from: pasteFrom, to: pasteTo, $from: $pasteFrom } = view.state.selection;
+    if (
+      sourceType?.isInSet($pasteFrom.marks()) &&
+      !pastedText.includes("\n") &&
+      collectComposerPromptInlineTokens(`${pastedText}\n`).length === 0
+    ) {
+      view.dispatch(
+        markAsClipboardEdit(
+          view.state.tr.insertText(pastedText, pasteFrom, pasteTo),
+          "paste",
+        ).scrollIntoView(),
+      );
+      return true;
+    }
+    const importFragment = readCallbacks().importContextFragment;
+    let text =
+      !literalText && importFragment
+        ? importPastedComposerText(clipboardData, importFragment)
+        : pastedText;
+    const tokens = literalText ? [] : collectComposerPromptInlineTokens(`${text}\n`);
+    const isChip = (token: (typeof tokens)[number] | undefined) =>
+      token?.type === "mention" ||
+      (token?.type === "skill" && skillLabelFor(token.value) !== null) ||
+      (token?.type === "model" && isKnownModel(token.instanceId, token.model));
+    const lastToken = tokens.at(-1);
+    if (isChip(lastToken) && lastToken?.end === text.length) {
+      text += " ";
+    }
+    if (isChip(tokens[0]) && tokens[0]?.start === 0) {
+      const map = serializeEditorDoc(view.state.doc);
+      const offset = flatToMarkdown(map, pmToFlat(map, view.state.selection.from));
+      if (offset > 0 && !/\s/.test(map.value[offset - 1]!)) text = ` ${text}`;
+    }
+    const { $from } = view.state.selection;
+    const lineBefore = $from.parent.textBetween(0, $from.parentOffset, undefined, "\uFFFC");
+    const literalLength = literalText
+      ? 0
+      : pastedPathQueryLength(lineBefore, text, readCallbacks().isPathQueryActive?.());
+    const editorInstance = (view.dom as TiptapEditorHTMLElement).editor;
+    if (editorInstance) {
+      const $paste = view.state.selection.$from;
+      const nested = ["listItem", "taskItem", "blockquote"].some((name) =>
+        hasAncestor($paste, name),
+      );
+      insertMarkdownParagraphs(
+        text,
+        skillLabelFor,
+        { styling: richText, blocks: !nested, literalText, literalLength, isKnownModel },
+        (content) => {
+          editorInstance
+            .chain()
+            .command(({ tr }) => {
+              markAsClipboardEdit(tr, "paste");
+              return true;
+            })
+            // Pasted chips and lines would split shown Markdown, so parse it first.
+            .command(collapseShownMarkdownSource)
+            .insertContent(content)
+            .command(({ tr }) => {
+              // Move after a pasted rule so the next keystroke cannot replace it; add a trailing line
+              // if needed.
+              const { selection } = tr;
+              if (!(selection instanceof NodeSelection) || !selection.node.isBlock) {
+                return true;
+              }
+              if (!tr.doc.resolve(selection.to).nodeAfter?.isTextblock) {
+                tr.insert(selection.to, tr.doc.type.schema.nodes.paragraph!.create());
+              }
+              tr.setSelection(TextSelection.create(tr.doc, selection.to + 1));
+              return true;
+            })
+            .run();
+        },
+      );
+      scrollTiptapCaretIntoView(editorInstance);
+    }
+    return true;
+  };
+
   const editor = useEditor(
     {
       extensions: richText ? RICH_TEXT_EXTENSIONS : PLAIN_TEXT_EXTENSIONS,
@@ -1107,6 +1202,9 @@ function ComposerPromptEditorTiptapInner(
         isKnownModel: (instanceId, model) => modelKeys.has(modelMentionKey(instanceId, model)),
       }),
       editable: !disabled,
+      // handlePaste parses pasted markdown itself and tags the insert as a paste for undo grouping, so Tiptap's
+      // paste rules would parse that result a second time and turn literal `*` and `**` into marks.
+      enablePasteRules: false,
       editorProps: {
         attributes: editorAttributes,
         handleKeyDown: (view, event) => {
@@ -1364,100 +1462,24 @@ function ComposerPromptEditorTiptapInner(
         handlePaste: (view, event) => {
           const clipboardData = event.clipboardData;
           if (!clipboardData || clipboardData.files.length > 0) return false;
-          const pastedText = clipboardData.getData("text/plain");
-          if (!pastedText) return false;
+          if (!insertClipboardText(view, clipboardData)) return false;
           event.preventDefault();
-          // Paste verbatim inside fences; markdown parsing would split blocks and create unsupported chips.
-          if (isInCodeBlock(view)) {
-            const { from, to } = view.state.selection;
-            view.dispatch(
-              markAsClipboardEdit(
-                view.state.tr.insertText(pastedText, from, to),
-                "paste",
-              ).scrollIntoView(),
-            );
-            return true;
-          }
-          // Shown Markdown source is parsed when the caret leaves, so paste one line into it as text.
-          const sourceType = view.state.schema.marks[MARKDOWN_SOURCE_MARK];
-          const { from: pasteFrom, to: pasteTo, $from: $pasteFrom } = view.state.selection;
-          if (
-            sourceType?.isInSet($pasteFrom.marks()) &&
-            !pastedText.includes("\n") &&
-            collectComposerPromptInlineTokens(`${pastedText}\n`).length === 0
-          ) {
-            view.dispatch(
-              markAsClipboardEdit(
-                view.state.tr.insertText(pastedText, pasteFrom, pasteTo),
-                "paste",
-              ).scrollIntoView(),
-            );
-            return true;
-          }
-          const importFragment = readCallbacks().importContextFragment;
-          let text =
-            !literalText && importFragment
-              ? importPastedComposerText(clipboardData, importFragment)
-              : pastedText;
-          const tokens = literalText ? [] : collectComposerPromptInlineTokens(`${text}\n`);
-          const isChip = (token: (typeof tokens)[number] | undefined) =>
-            token?.type === "mention" ||
-            (token?.type === "skill" && skillLabelFor(token.value) !== null) ||
-            (token?.type === "model" && isKnownModel(token.instanceId, token.model));
-          const lastToken = tokens.at(-1);
-          if (isChip(lastToken) && lastToken?.end === text.length) {
-            text += " ";
-          }
-          if (isChip(tokens[0]) && tokens[0]?.start === 0) {
-            const map = serializeEditorDoc(view.state.doc);
-            const offset = flatToMarkdown(map, pmToFlat(map, view.state.selection.from));
-            if (offset > 0 && !/\s/.test(map.value[offset - 1]!)) text = ` ${text}`;
-          }
-          const { $from } = view.state.selection;
-          const lineBefore = $from.parent.textBetween(0, $from.parentOffset, undefined, "\uFFFC");
-          const literalLength = literalText
-            ? 0
-            : pastedPathQueryLength(lineBefore, text, readCallbacks().isPathQueryActive?.());
-          const editorInstance = (view.dom as TiptapEditorHTMLElement).editor;
-          if (editorInstance) {
-            const $paste = view.state.selection.$from;
-            const nested = ["listItem", "taskItem", "blockquote"].some((name) =>
-              hasAncestor($paste, name),
-            );
-            insertMarkdownParagraphs(
-              text,
-              skillLabelFor,
-              { styling: richText, blocks: !nested, literalText, literalLength, isKnownModel },
-              (content) => {
-                editorInstance
-                  .chain()
-                  .command(({ tr }) => {
-                    markAsClipboardEdit(tr, "paste");
-                    return true;
-                  })
-                  // Pasted chips and lines would split shown Markdown, so parse it first.
-                  .command(collapseShownMarkdownSource)
-                  .insertContent(content)
-                  .command(({ tr }) => {
-                    // Move after a pasted rule so the next keystroke cannot replace it; add a trailing line
-                    // if needed.
-                    const { selection } = tr;
-                    if (!(selection instanceof NodeSelection) || !selection.node.isBlock) {
-                      return true;
-                    }
-                    if (!tr.doc.resolve(selection.to).nodeAfter?.isTextblock) {
-                      tr.insert(selection.to, tr.doc.type.schema.nodes.paragraph!.create());
-                    }
-                    tr.setSelection(TextSelection.create(tr.doc, selection.to + 1));
-                    return true;
-                  })
-                  .run();
-              },
-            );
-            scrollTiptapCaretIntoView(editorInstance);
-          }
           return true;
         },
+        handleDrop: (view, event, _slice, moved) => {
+          const data = event.dataTransfer;
+          if (moved || view.dragging || !data || data.files.length > 0) return false;
+          // ProseMirror already parses an HTML drop into marks; only plain-text drops need Markdown parsing.
+          if (!data.getData("text/plain") || data.getData("text/html")) return false;
+          const target = view.posAtCoords({ left: event.clientX, top: event.clientY });
+          if (!target) return false;
+          view.dispatch(
+            view.state.tr.setSelection(TextSelection.near(view.state.doc.resolve(target.pos))),
+          );
+          // Handling the drop skips ProseMirror's own focus call, so typing would go to the previous control.
+          view.focus();
+          return insertClipboardText(view, data);
+        },
       },
       onUpdate: ({ editor: updated, transaction }) => {
         // Undo can restore a chip for a skill or model the environment no longer offers.
diff --git a/apps/web/src/composer-rich-text-doc.ts b/apps/web/src/composer-rich-text-doc.ts
index 417397e88ccc5..256d46fc63ecb 100644
--- a/apps/web/src/composer-rich-text-doc.ts
+++ b/apps/web/src/composer-rich-text-doc.ts
@@ -16,14 +16,13 @@ import { Blockquote } from "@tiptap/extension-blockquote";
 import { CodeBlock } from "@tiptap/extension-code-block";
 import { Heading } from "@tiptap/extension-heading";
 import { HorizontalRule } from "@tiptap/extension-horizontal-rule";
-import { Italic, starInputRegex, starPasteRegex } from "@tiptap/extension-italic";
+import { Italic, starInputRegex } from "@tiptap/extension-italic";
 import {
   type Command,
   type Editor,
   Extension,
   InputRule,
   markInputRule,
-  markPasteRule,
   mergeAttributes,
 } from "@tiptap/core";
 import { BulletList, ListItem, OrderedList } from "@tiptap/extension-list";
@@ -309,9 +308,6 @@ export const ComposerItalicExtension = Italic.extend({
   addInputRules() {
     return [markInputRuleOutsideCode(starInputRegex, this.type)];
   },
-  addPasteRules() {
-    return [markPasteRule({ find: starPasteRegex, type: this.type })];
-  },
 });
 
 export const ComposerBoldExtension = Bold.extend({