GL-334: Fix startup gate bypass + make /readiness probe real DB and Redis

[discodone]

Review source

Round 14 (Opus 4.8 + Gemini) — P0/P1. Startup gate is bypassable, readiness probe lies.

Problem

1. startup_errors() runs only in backend/main.py. Running uvicorn backend.src.api.app:app (the standard ASGI invocation that DEPLOYMENT docs reference for workers) skips ALL production config validation. You can boot in production mode with placeholder secrets and demo endpoints on.
2. /readiness (health.py:87) only validates runtime config, not DB or Redis. A pod with a dead database reports ready and takes traffic. The DB check lives in /health (liveness), which is backwards — liveness failure restarts the pod instead of draining it.

Fix

• Call startup_errors() inside the app lifespan (app.py) so it fails fast regardless of entrypoint
• Move DB + Redis connectivity check from /health into /readiness; /readiness returns 503 when either is down
• /health (liveness) should only check the process is alive, not dependencies

Acceptance Criteria

• Booting via uvicorn ...app:app with placeholder secrets in production mode fails at startup
• /readiness returns 503 when DB is down
• /readiness returns 503 when Redis is down
• /health stays 200 even when DB is down (liveness vs readiness)
• mypy clean, ruff clean, tests >= baseline