## What
Cache the Timmy agent instance at app startup (in lifespan) instead of creating a new one per `/serve/chat` request.
## Changes
- `src/timmy_serve/app.py`: Create agent in lifespan, store in `app.state.timmy`
- `tests/timmy/test_timmy_serve_app.py`: Updated tests for lifespan-based caching, added `test_agent_cached_at_startup`
2085 unit tests pass. 2102 pre-push tests pass. 78.5% coverage.
Closes#471
Co-authored-by: Timmy <timmy@timmytime.ai>
Reviewed-on: http://localhost:3000/rockachopa/Timmy-time-dashboard/pulls/476
Co-authored-by: Timmy Time <timmy@Alexanderwhitestone.ai>
Co-committed-by: Timmy Time <timmy@Alexanderwhitestone.ai>