feat(tabs): start a session beside any tab from an opt-in + in its actions

docs/wiki/Settings-Reference.md

@@ -121,6 +121,7 @@ memory. Messages expire 12 hours after they were posted either way. See
 | Tall Tabs              | Taller tab strip.                                                                          |
 | CLI Logos on Tabs      | Each agent tab, and its row on the desktop home rail, shows the CLI's logo before the name. Off hides those logos on this device; the status dot and the shell's SH badge stay, and tiles, split headers and the Run menus keep their logos. On by default. |
 | Pop-out Button on Tabs | Adds the detach control to tabs, with a per-tab override.                                  |
+| New Session Button on Tabs | Adds a **+** beside each tab's gear: pick a CLI the tab's case can start and one session starts in that case (or worktree) and named group, leaving the Run button alone. The row menu offers it as *New session here…*. Per device, off by default. See [The Dashboard](The-Dashboard#session-tabs). |
 | Spawn Lineage Lines    | Lines from each tab to the sessions it spawned; the selected tab's family is drawn thicker. Desktop only, on by default. |
 | Auto-name Sessions     | Titles a new tab after its first prompt, keeping the case prefix (`w3-myapp: fix the login redirect`). Synced, off by default. See [The Dashboard](The-Dashboard#automatic-session-names). |
 | Spawned Tabs Follow Their Parent | A session started by another one (an agent's worker, a `parentSessionId` spawn) follows its parent's tab into its group and moves with it until you move it by hand; the row menu then says where it sits and offers *Follow parent again*. Off, it starts right after its parent and stays put. Decided when the tab is created, so flipping it leaves existing tabs alone. Synced, off by default. |

docs/wiki/The-Dashboard.md

@@ -77,6 +77,14 @@ An agent tab shows its CLI's logo before the name, and a shell tab an `SH` badge
 on Tabs** (App Settings → Appearance → Tabs) hides the logos on that device; the tile and split
 headers and the Run menus keep theirs.
 
+**New Session Button on Tabs** (same place, per device, off by default) adds a **+** beside
+the tab's gear. It lists the CLIs that tab's case can start, each with its logo and name (a
+Docker case lists what its container has), and a pick starts one session in that tab's case,
+or the worktree it runs in, and in its named group. The Run button keeps its own mode and case.
+Wherever a tab has a row menu (the vertical rail, the sidebar, `Shift+F10` on a grouped row),
+the same list is its **New session here…** entry. From a tab outside any named group, the new
+session lands in the case's default group if the case has one, as a Run from the toolbar does.
+
 **Status is carried by the dot and the tab's own styling:**
 
 | Look                          | Meaning                                                                 |

src/web/CLAUDE.md

@@ -34,7 +34,7 @@ Frontend JS modules have `@fileoverview` with `@dependency`/`@loadorder` tags. L
 
 **Entrance animations** (`entrance-animations.js`, all OFF by default): opt-in animations for tabs, terminal, windows, connection lines and tile-grid tiles, chosen via `data-tab-anim` / `data-term-anim` / `data-win-anim` / `data-line-anim` / `data-tile-anim` on `<html>`; the default `legacy` theme short-circuits every hook (tiles keep the grid's own `settle`). ⚠️ Tabs and lines are destroyed mid-animation on re-render, so re-apply to the fresh element by id with a negative `animation-delay` (resume, never restart). ⚠️ Terminal-pane styles may animate only transform / opacity / clip-path (anything else resizes the PTY via FitAddon); `blur` is the ONE sanctioned `filter` exception, do not generalise it. ⚠️ Line glow lives in `--line-glow` so blur keyframes interpolate. Every animation setting lives in App Settings → **Animations** (`#settings-animations`); put new ones there. ⚠️ Tiles are OFF by default (Animations → Tile Animations, default `settle` = the grid's own fade, no screen beat); a theme only presets it. A tile's FRAME animates transform/opacity only (six at once, no filter) with `tile-enter*`/`tile-leave*` keyframe names (what the mount and the still copy listen for); its SCREEN replays the pane style on `.tile-body.term-enter`; a reload's restore always settles. Persisted per-device in `codeman:*Anim` localStorage keys, never in `SettingsUpdateSchema`; lab at `?animlab=1`. Test: `test/entrance-animations.test.ts`. → [architecture-invariants#entrance-animations](../../docs/architecture-invariants.md#entrance-animations)
 
-**Mobile tab strip scrolling** (issue #257): under 768px the tab strip scrolls horizontally, so the active tab must be kept reachable. `_updateActiveTabImmediate()` reveals it via `computeTabScrollLeft()` (constants.js, rect math on the strip's own `scrollLeft`, never `scrollIntoView()`, which scrolls the document under the fixed header); `_fullRenderSessionTabs()` must restore `scrollLeft` across rebuilds and re-reveal only when the active tab changed (`_lastRenderedActiveTabId`) or, grouped by state, the ACTIVE tab moved to another state band (`_noteActiveTabBand()`, both render paths, scrolling row only; another tab's move never scrolls). ⚠️ The phone-block `min-width` on `.session-tab.active .tab-name` keeps the tab's centre off the gear/close icons, sized for numberless tabs 10+ (floor 40px); do not shrink it. ⚠️ Never reintroduce hoisting the active session to the front of the strip. Tests: `test/mobile-tab-tap-zones.test.ts`, `test/tab-triage.test.ts`. → [architecture-invariants#mobile-tab-strip-scrolling](../../docs/architecture-invariants.md#mobile-tab-strip-scrolling)
+**Mobile tab strip scrolling** (issue #257): under 768px the tab strip scrolls horizontally, so the active tab must be kept reachable. `_updateActiveTabImmediate()` reveals it via `computeTabScrollLeft()` (constants.js, rect math on the strip's own `scrollLeft`, never `scrollIntoView()`, which scrolls the document under the fixed header); `_fullRenderSessionTabs()` must restore `scrollLeft` across rebuilds and re-reveal only when the active tab changed (`_lastRenderedActiveTabId`) or, grouped by state, the ACTIVE tab moved to another state band (`_noteActiveTabBand()`, both render paths, scrolling row only; another tab's move never scrolls). ⚠️ The phone-block `min-width` on `.session-tab.active .tab-name` keeps the tab's centre off the gear/close icons, sized for numberless tabs 10+ (floor 40px); do not shrink it. With the opt-in tab "+" on (`showTabNewButton`, `html.tabs-show-new`) a third icon joins them and the reserve grows to 68px, still under the 80px `max-width`. ⚠️ Never reintroduce hoisting the active session to the front of the strip. Tests: `test/mobile-tab-tap-zones.test.ts`, `test/tab-triage.test.ts`. → [architecture-invariants#mobile-tab-strip-scrolling](../../docs/architecture-invariants.md#mobile-tab-strip-scrolling)
 
 **Session list layout: header strip or left sidebar** (`sessionListLayout`, default `header`; per-device via `displayKeys`, also in `SettingsUpdateSchema`): the list can move into a collapsible `<aside>` (Alt+B, `toggleSessionSidebar`) or, via `tabOrientation`, a resizable vertical `#tabRail` (desktop/tablet only). ⚠️ There is ONE `#sessionTabs`, MOVED between hosts, never a second list: `applySessionListLayout()` runs first, then `applyTabOrientation()`, both BEFORE `applyTabWrapSettings()`, and both arm/disarm `_startSidebarRichClock()`. ⚠️ Axis decisions use `_isVerticalTabList()`, never `isSessionSidebarActive()` alone. ⚠️ Rich rows share one gate, `isRichTabRows()`; rich CSS pairs sidebar+rail with comma-grouped selectors, never `:is()`, and card rules stay rail-scoped. ⚠️ Rail sort (`tabRailSort`, default `activity`) is the flex `order` property only, never a DOM reorder; the arrow-key walk and the phone swipe follow computed `order`. ⚠️ Leaving sidebar mode clears `_sidebarFilter`; the handheld overlay drawer is `inert` when closed, the docked rail never. ⚠️ The rail's **Search sessions** box (`setTabRailSearch`, in memory only) and the sidebar filter share ONE row filter, `_applyTabListFilter()` over the pure `CodemanTabSearch` (constants.js): classes only, never a reorder or layout write; the rail matches the name, the sidebar name + folder. ⚠️ A session row with a tab alert (`tabAlerts`, red or yellow) is never hidden by either box: it goes in as `keep: true`, counts toward its group (which stays on screen) but not toward `matchCount`. ⚠️ Escape in the rail box is claimed by the global capture-phase Escape branch (the box's own `onkeydown` runs after it, too late to stop `closeAllPanels()`), and a filter change that shows or hides anything redraws the connector lines, since a keystroke re-renders nothing; a floating window finds its parent tab only through `_paintedSessionTab()` (a hidden row's rect is all zero but truthy, which drew connectors from the viewport's corner). While it runs `_projectTabGroups()` projects every group open (a collapsed group's rows are not in the DOM) and `toggleTabGroupCollapsed()` refuses, leaving the stored collapse untouched; drag stays on during a search (owner decision), a drop landing between the visible neighbours; `applyTabOrientation()` clears it off the rail. Tests: `test/tab-rail-search.test.ts`, `test/tab-rail-search.browser.test.ts`. → [architecture-invariants#session-list-layout-header-strip-vs-left-sidebar](../../docs/architecture-invariants.md#session-list-layout-header-strip-vs-left-sidebar)