Resolves #410.

This PR implements the second approach outlined in the issue to fix the flaky focus assertion on the login provider picker screen:

Separation of Concerns: Removed the flaky assert search.has_focus check from the data filtering test (test_tui_login_api_provider_picker_filters_by_name_and_display_name), as filtering behavior doesn't rely on focus states. Changed pilot.pause() calls to pilot.wait_for_scheduled_animations() to flush asynchronous filter events reliably.

Dedicated Focus Test: Added a dedicated autofocus test (test_tui_login_provider_search_autofocus) that utilizes native event flushing to test focus state behavior independently.

The isolated tests passed completely clean locally across consecutive test runs.

cc @ShreyanshVaibhaw — since this issue primarily popped up on your environment, could you check out this branch and verify if it permanently kills the flake on your machine?

Bash

git fetch origin
git checkout fix-flaky-tui-focus
uv run pytest "tests/test_tui_app.py::test_tui_login_api_provider_picker_filters_by_name_and_display_name"
uv run pytest "tests/test_tui_app.py::test_tui_login_provider_search_autofocus"
#original test :-
uv run pytest "tests/test_tui_app.py::test_tui_login_api_provider_picker_filters_by_name_and_display_name" -q