[Bug]: Error asks to 'press Stop' to switch model/provider, but no Stop button is shown when thread is idle #36450

Before submitting

• I searched existing issues and did not find an open duplicate addressing this UI dead end. Related: [Bug]: A send that would release a session's background work is refused, though the same message queued behind a turn is accepted #32296 (server queueing semantics), [Bug]: Stop does not lift the background-work guard: provider/model switch stays refused ("press Stop" is a dead end) #35240 (closed without resolution), [Bug]: Claude is still running background agents or commands, and this model or setting change would end them. Wait for them to finish, or press Stop, then send the message again. #16073 (partially resolved for in-provider setting changes).
• I included enough detail to reproduce or investigate the problem.

Area

apps/desktop

Steps to reproduce

1. In a thread, let the agent start background work (background tasks, subagent, or commands).
2. Wait for the main agent's turn to complete / settle so the thread is idle (no active streaming run).
3. Switch the model or provider from the model picker in the composer.
4. Try to send a message.
5. The message is refused with:

   The previous provider is still running background agents or commands, and switching would end them. Wait for them to finish, or press Stop, then send the message again.

Expected behavior

If the error message instructs the user to "press Stop":

1. The UI should display an accessible Stop control (e.g. a persistent Stop button in the composer or header while background work is active, or a dedicated "Stop background work" button).
2. Ideally, the error banner itself should offer a one-click action: "Stop background work & switch" or "Queue behind background tasks".

Actual behavior

• The UI only displays a Stop button while a foreground turn is actively running/streaming.
• Once the main turn is finished, the composer returns to its idle state, and no Stop button is rendered anywhere in the interface.
• As a result, the user is trapped in a dead end: they are instructed to press Stop, but have no way to do so, leaving them completely unable to switch models or providers.

Impact

Blocks work completely

Environment

• Platform: Windows x64 (also reproduces across desktop and web clients)
• Version: T3 Code 0.1.10-nightly (and earlier versions)

Workaround

Starting a completely new thread or manually editing the underlying database state.