Desktop app: session list activity dot keeps pulsing on an idle session with no running tasks

Environment

• Claude Code desktop app (macOS), app bundle version 1.0 ("Claude Code.app")
• macOS 26.5.1 (Darwin 25.5.0)
• Model: claude-fable-5

Bug

The activity indicator dot next to a session in the sidebar session list keeps pulsing indefinitely even though the session is fully idle:

• the assistant's turn had ended normally (final summary message delivered),
• all background Bash tasks in the session had completed and reported back,
• TaskList was empty,
• no session-owned processes were running.

The session's work was done and committed; nothing should have been signaling activity.

Expected

The pulsing dot should clear once the session goes idle (turn ended, no running background tasks), or at latest when the session is opened/read.

Actual

The dot continues pulsing. Opening other sessions / time passing did not clear it.

Possibly relevant context

• Two Claude Code sessions were running concurrently against the same project directory (same repo, two agents coordinating). The stale dot appeared on the completed session while the other session was still active — the indicator may be picking up sibling-session or project-level activity instead of per-session state.
• The completed session had used background tasks (run_in_background Bash) heavily during the turn; all had finished and delivered their completion notifications before the turn ended.

Repro sketch

1. Open two sessions in the same project in the desktop app.
2. In session A, run a task that uses several background Bash commands, let it finish completely (turn ends).
3. Keep session B actively working.
4. Observe session A's sidebar dot: it keeps pulsing despite A being idle.

Reported on behalf of the user from within the affected session.