feat(T1.8): implement health checks for Kubernetes deployment

- Add internal/health package with health checker
- Implement three endpoints: /health, /health/live, /health/ready
- /health returns full JSON report with component status, latency, timestamp
- /health/live for K8s liveness probe (service running)
- /health/ready for K8s readiness probe (ready to accept traffic)
- Temporal connectivity check via GetWorkflow call with timeout
- Health check caching (30s interval) to prevent excessive checks
- Graceful shutdown: health server stops on SIGINT/SIGTERM
- Add --health flag to starter command to run health check
- Worker runs health server on port 8081 alongside task queue worker
- 10/10 unit tests passing
- All verification criteria met

Closes T1.8

cmd/worker/main.go

@@ -1,13 +1,20 @@
 package main
 
 import (
+	"context"
 	"fmt"
 	"log"
+	"net/http"
+	"os"
+	"os/signal"
+	"syscall"
+	"time"
 
 	"go.temporal.io/sdk/client"
 	"go.temporal.io/sdk/worker"
 	"github.com/rockliang/poimen/workflows/action"
 	"github.com/rockliang/poimen/workflows/internal/config"
+	"github.com/rockliang/poimen/workflows/internal/health"
 	"github.com/rockliang/poimen/workflows/statemachine"
 )
 
@@ -55,9 +62,53 @@ func main() {
 	// w.RegisterActivity(action.UpdateLessonsActivity)
 	// w.RegisterActivity(action.ReadLessonsActivity)
 
-	// Run worker
-	fmt.Println("Starting worker on queue 'poimen-taskqueue'...")
-	if err := w.Run(worker.InterruptCh()); err != nil {
+	// Initialize health checker
+	healthChecker := health.NewChecker(c)
+	healthHandler := health.NewHandler(healthChecker)
+
+	// Set up HTTP server for health checks
+	mux := http.NewServeMux()
+	healthHandler.RegisterRoutes(mux)
+
+	healthServer := &http.Server{
+		Addr:    ":8081",
+		Handler: mux,
+	}
+
+	// Start health check server in a goroutine
+	go func() {
+		log.Printf("Health check server listening on %s", healthServer.Addr)
+		if err := healthServer.ListenAndServe(); err != nil && err != http.ErrServerClosed {
+			log.Printf("health check server error: %v", err)
+		}
+	}()
+
+	// Set up signal handling for graceful shutdown
+	sigChan := make(chan os.Signal, 1)
+	signal.Notify(sigChan, syscall.SIGINT, syscall.SIGTERM)
+
+	// Run worker in a goroutine
+	workerErrChan := make(chan error, 1)
+	go func() {
+		fmt.Println("Starting worker on queue 'poimen-taskqueue'...")
+		if err := w.Run(worker.InterruptCh()); err != nil {
+			workerErrChan <- err
+		}
+	}()
+
+	// Wait for either worker error or signal
+	select {
+	case err := <-workerErrChan:
 		log.Fatalf("worker failed: %v", err)
+	case sig := <-sigChan:
+		log.Printf("received signal: %v, shutting down gracefully", sig)
+		w.Stop()
+
+		// Shutdown health check server
+		ctx, cancel := context.WithTimeout(context.Background(), 10*time.Second)
+		defer cancel()
+		if err := healthServer.Shutdown(ctx); err != nil {
+			log.Printf("health check server shutdown error: %v", err)
+		}
 	}
 }