[Enhancement] Add Health Check for Each Service Dependency #24

Problem

Health checks exist but don't verify connectivity to dependencies comprehensively

Impact

• Services report as "ready" even if dependencies unreachable
• Deployments fail silently
• No way to detect configuration issues early

Solution

Implement proactive dependency checks in readiness probes

Acceptance Criteria

• MongoDB connectivity verified
• Redis connectivity verified
• RabbitMQ connectivity verified
• Timeout handling implemented