* fix(status-bar): invalidate the CLI session count on kill and restart
`pty:management:killOne` / `killAll` / `restart` tear sessions down via `adapter.shutdown()` and broadcast nothing — unlike `pty:kill`, which ends in `sendPtyExitToRenderer`. The status-bar count is an event-sourced cache, so killing sessions from Manage Sessions or "Kill all terminals" left the `>_ N` chip frozen until the popover was opened, which itself triggers a refresh.
> [!NOTE]
> The dual-source split described in the issue text was already fixed by merged #9387. This closes a *different* remaining invalidation gap that produces the same reported symptom.
Broadcast the teardown so the chip updates without needing the popover opened.
Fixes#8372
Co-authored-by: Orca <help@stably.ai>
* test(e2e): add recordable proof for status-bar-cli-session-count
Fails on origin/main, passes on this branch.
Test: drops after Manage Sessions kills a foreign daemon session, popover never opened
Co-authored-by: Orca <help@stably.ai>
* fix(status-bar): avoid duplicate inventory refresh after kill all
---------
Co-authored-by: Orca <help@stably.ai>
69ca9f91b3