Improve Health Check and Service Startup Flow

[alexluong]

Currently, services can appear "ready" while having connection issues to dependencies (e.g. Redis timeout). We should enhance the health check and startup flow to properly verify all critical dependencies are connected before marking a service as ready. This should include proper readiness probes for k8s, connection retries with backoff, and clear error reporting when dependencies aren't available. This will prevent silent failures where services appear healthy but aren't fully operational.

Specifically, for API service, we run a few different things: API router, publishmq consumer, retrymq consumer. If one of the consumer fails, there's an error log line but we don't escalate it further.