fix(tui): use running state for app lifecycle guards

[ousamabenyounes]

Summary

• Replaces app-level self.is_mounted truthiness guards with self.is_running in the TUI lifecycle paths.
• Leaves the existing widget-level widget.is_mounted safety check unchanged.
• Adds a regression test proving a not-running app returns before querying or rescheduling focus work.

Closes #894.

Test verification (RED -> GREEN)

RED on origin/main with only the regression test added:

$ uv run pytest tests/test_tui_app_lifecycle.py -q
F                                                                        [100%]
AttributeError: 'types.SimpleNamespace' object has no attribute '_focus_chat_input'
1 failed in 4.80s

GREEN after the fix:

$ uv run pytest tests/test_tui_app_lifecycle.py tests/test_proxy_renderer.py -q
....                                                                     [100%]
4 passed in 4.79s

Local CI replay:

$ ./run-ci.sh
....                                                                     [100%]
4 passed in 4.80s
All checks passed!
2 files already formatted
Success: no issues found in 1 source file

Known baseline:

$ uv run mypy strix/interface/tui/app.py
38 pre-existing Textual typing errors in strix/interface/tui/app.py

$ uv run pyright strix/interface/tui/app.py
117 pre-existing Textual typing/private-usage errors in strix/interface/tui/app.py

[greptile-apps]

Greptile Summary

This PR corrects TUI lifecycle guards to use the application running state.

• Replaces app-level is_mounted checks with is_running across splash, focus, rendering, action, and resize paths.
• Preserves widget-level mount checks for individual widget safety.
• Adds a regression test confirming focus work is neither queried nor rescheduled after the app stops.

Confidence Score: 5/5

The PR appears safe to merge with no actionable correctness or security issues identified.

The lifecycle changes consistently prevent application-level UI work after the Textual app has stopped, while existing widget mount checks continue to protect operations on individual widgets.

Important Files Changed

Filename	Overview
strix/interface/tui/app.py	Replaces inappropriate app-level mount-state guards with running-state guards while retaining widget-specific mount checks; no actionable defect was identified.
tests/test_tui_app_lifecycle.py	Adds a focused regression test proving that a stopped app returns before querying widgets or scheduling additional focus work.

_{Reviews (1): Last reviewed commit: "fix(tui): use running state for app life..." | Re-trigger Greptile}