refactor(tui): inject dependencies into EventHandlerRegistry instead of app reference

[Kohei-Wada]

Summary

Removes the tight coupling between EventHandlerRegistry / WebSocketHandler and the TaskdogTUI app class by injecting individual callables instead of the whole app instance. This aligns these services with the dependency-injection style already used by TaskUIManager.

Closes #772.

Changes

• event_handler_registry.py: drop the app parameter; inject notify, reload_tasks, set_client_id, get_client_id. Add a NotifyFn Protocol for the notify signature. The _reload_tasks method is replaced by the injected callable of the same name.
• websocket_handler.py: accept the same four callables and forward them to the registry; no longer holds an app reference.
• app.py: wire the callables when constructing WebSocketHandler (get_client_id is lambda: self.api_client.client_id).
• tests: inject mock callables instead of mock_app; remove the obsolete task_ui_manager is None test (the registry no longer touches task_ui_manager).

Deviation from the proposal

The proposed schedule_fn (for call_later) is not injected: the registry never calls call_later, so adding it would be dead weight.

Verification

• grep -r "self\.app" .../event_handler_registry.py → 0 matches
• grep -r "self\.app" .../websocket_handler.py → 0 matches
• make check → passed (lint + typecheck + codespell + vulture)
• make test-ui → 1095 passed

[amazon-q-developer]

The refactoring successfully decouples EventHandlerRegistry and WebSocketHandler from the TaskdogTUI app class by injecting specific callables. The dependency injection pattern is correctly implemented across all files, tests are properly updated, and the changes maintain functional correctness. No defects blocking merge identified.

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