fix(tui): drain background process completion notifications

[Ade5954]

Root cause: the TUI server (tui_gateway/server.py) never drained process_registry.completion_queue, so notify_on_complete events from background processes were silently lost. CLI mode drains the queue in both its idle loop and after-turn paths; gateway mode uses async watcher tasks. Neither path existed for TUI mode.

Fix: after run_conversation() returns in _run_prompt_submit, drain completion_queue and auto-submit formatted notifications as follow-up turns. Follows the exact same pattern as the existing goal continuation code — release session.running in the outer finally, then re-acquire and call _run_prompt_submit with the synthetic notification text.

Uses _format_process_notification from cli (already imported elsewhere in the TUI server via the same lazy-import pattern).

Why Option 1 (After-turn drain)?

Three approaches were proposed in the issue. Option 1 was chosen because:

1. Minimal & localized — 37 lines in a single file ( tui_gateway/server.py ). No new threads, no lifecycle management.
2. Proven pattern — the exact same follow-turn dispatch already exists for goal continuation. Just replicate it.
3. CLI parity — CLI mode drains completion_queue after each agent turn (cli.py L13264). TUI now does the same.
4. Right timing — after-turn is the right moment: the agent just finished a turn, so it's ready to learn about completed background processes.
5. Cheap — the queue is almost always empty; no polling overhead.
   Option 2 (polling thread) was rejected as over-engineering. Option 3 (shared helper) was unnecessary since _format_process_notification from cli.py is already importable directly.

How the Fix Works

After run_conversation() returns in _run_prompt_submit :

1. Drain process_registry.completion_queue
2. Skip events already consumed by wait() / poll() / log() (prevents duplicates)
3. Format each completion into a [IMPORTANT: ...] message using _format_process_notification() from cli.py
4. Dispatch as a synthetic follow-up turn via _run_prompt_submit — same lock/release pattern as goal continuation
5. If session is already busy (user jumped in mid-drain), put the event back and break — it'll be picked up on the next turn

Related Issue

Closes #26071

Type of Change

• 🐛 Bug fix (non-breaking change that fixes an issue)

Checklist

Code

• I've read the Contributing Guide
• My commit messages follow Conventional Commits (fix(scope):, feat(scope):, etc.)
• I searched for existing PRs to make sure this isn't a duplicate
• My PR contains only changes related to this fix/feature (no unrelated commits)
• I've run pytest tests/ -q and all tests pass
• I've added tests for my changes (required for bug fixes, strongly encouraged for features)
• I've tested on my platform:

[alt-glitch]

Superseded by #26327 (merged). Thanks for the initial approach — the merged PR builds on it with an autonomous poller thread in addition to the after-turn drain.