When a turn ends but Claude leaves something running, the session isn't really idle. Two cases: a watcher (the Monitor tool waits for a log line, a file, a build), or background tasks (a shell or subagent still going). Main shows a card above the composer with an eye or a block grid, the copy, and Stop. Stop ends the Claude process, so watchers and tasks die. Your conversation stays.
This page fits that into the new composer, next to the goal bars, the context warning and the live status header. Every phone is live: tap Stop, the header icon (C), or the chip (D).
It works, but it's the one notice that doesn't use the bar pattern, and its full Button gives Stop more weight than anything else above the field. Stacked with a goal and the context warning, it's a third shape in the same column.
Each option shows the watcher alone, then the busy case: a goal in progress and context at 84%. Switch Running above to see background tasks, and Tone for grey vs the blue that tool calls use in the transcript.
The status header already says "Working" during a turn. B lets it keep talking after the turn ends, so the composer tells one continuous story. Sending a message is allowed throughout. It starts a new turn, which is why the send button stays live next to Stop.
Same parts, wider column. Both shown with the context warning, so you can see how much space each one takes.
ComposerStatusHeader: show it when backgroundWork && !isProcessing(), glyph from the kind, plus a soft Stop beside send that calls the existing handleStop. No elapsed time: SessionInfo has no start time for background work, so adding one would mean server changes.