Add automated unit and mock integration test suite

- Configure conftest.py with pytest tmp_path DB isolation fixtures
- Add test_db.py for schema connection validations
- Add test_fetcher.py with mocked yt-dlp subprocess parser checks
- Add test_summarizer.py with mocked transcripts and Claude API requests
- Add test_main.py for FastAPI router endpoints and state updates

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

backend/requirements.txt

@@ -4,3 +4,6 @@ yt-dlp>=2023.0.0
 youtube-transcript-api>=0.6.0
 aiosqlite>=0.18.0
 httpx>=0.24.0
+pytest>=7.0.0
+pytest-asyncio>=0.21.0
+pytest-mock>=3.10.0