fix(runner): add health probes and improve INITIAL_PROMPT error logging

[maknop]

Summary

This PR implements health probes for runner pods and improves error logging for INITIAL_PROMPT retries, matching the implementation from ambient-code#1529.

Changes

Kubernetes Health Probes

• Added readiness probe to runner container (3s initial delay, 5s period)
• Added liveness probe to runner container (20s initial delay, 30s period)
• Probes check /health endpoint on the runner's FastAPI server

Error Logging Improvements

• Enhanced retry error logging in app.py to include exception type
• Previously logged empty strings for exceptions like asyncio.TimeoutError
• Now logs: "error: TimeoutError: <details>" instead of "error: "

Benefits

• Prevents premature traffic routing: Service won't route to pods until FastAPI is ready
• Reduces 503 errors: Eliminates "runner unavailable" errors during pod startup
• Better debugging: More informative error logs with exception types
• Self-healing: Liveness probe enables automatic pod restarts on failure

Test Plan

• Code compiles successfully (go vet passes)
• Code formatting is correct (gofmt passes)
• Deploy to test cluster and verify health probes are configured
• Verify no 503 errors during pod startup
• Verify error logs include exception types during connection failures

🤖 Generated with Claude Code