fix: emit runtime timing logs at info level

[afaryy]

Why

The public Cloud Run app records stage timing in code, but Python defaulted to WARNING and suppressed the INFO record before it reached Cloud Logging.

What changed

• Configure the runtime root logger at INFO during Cloud Run startup.
• Preserve existing handlers; add a default handler only when none exists.
• Add a regression test proving an INFO timing record reaches root handlers.

Privacy

The timing line contains only durations. It does not log concerns, case IDs, contact details, or model output.

Verification

• Python tests: uv run pytest -q — 281 passed
• Python lint: uv run ruff check src tests
• Frontend tests: run from frontend — 31 passed
• Frontend lint and production build: passed