Desktop UI shows Running status while the session is idle (no active turn, tool call, or background task)
Bug description
The session status indicator in the UI shows "Running" even when nothing is running — no in-flight tool call, no active turn, and no live background task. The session is actually idle (the assistant turn has ended and it is waiting for user input or a background-task notification), but the UI still presents it as actively working.
Environment
- Claude Code 2.1.201, desktop app host, macOS 26.5.2 (arm64)
- Observed in a long-lived session (many turns over ~2 days)
What the session looked like when observed
The session where this was observed had heavy use of Bash with run_in_background: true: many background tasks were started and completed over the course of the session (their completion notifications were delivered and handled). With all background tasks finished and the assistant turn ended, the UI still showed "Running". This suggests the status chip may not be returning to idle after turn end, or stale completed-background-task state keeps it pinned to "Running".
Expected
The status should reflect actual activity: "Running" only while a turn/tool call/background task is genuinely executing, and an idle/ready state otherwise.
Actual
"Running" persists while the session is idle with zero active tasks.
Repro sketch
- In the desktop app, run a session that starts several backgrounded Bash tasks (
run_in_background: true) and let them all complete. - Let the assistant finish its turn (no pending tool calls).
- Observe the session status indicator: it continues to show "Running" despite nothing executing.
(Reported by the user observing the UI; the agent side confirmed no tasks were live at the time.)
<img width="986" height="743" alt="Image" src="https://github.com/user-attachments/assets/557b364d-73e6-4a23-b44c-1579a12f4a22" />