Expose Prometheus metrics on a separate port

Metrics are served on METRICS_PORT (default 2112, "off" to disable), never on
the public port. Besides the Go runtime and process metrics this adds:

- http_requests_total and http_request_duration_seconds per route pattern,
  from an Echo middleware.
- musicserver_songs_requested_total and musicserver_songs_played_total by
  pick mode (random, low, classic). The mode is now stored with each queued
  song (migration 000006, not released yet).
- Library size, sync duration, last successful sync, broken songs from the
  last full sync, and the database connection pool.

Refs #35, #36, #37

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>

internal/server/server.go

@@ -12,7 +12,9 @@ import (
 	"music-server/internal/db"
 	"music-server/internal/db/repository"
 	"music-server/internal/logging"
+	"music-server/internal/metrics"
 
+	"github.com/prometheus/client_golang/prometheus"
 	"go.uber.org/zap"
 )
 
@@ -34,6 +36,8 @@ type Server struct {
 	stats      *backend.StatisticsService
 	search     *backend.SearchCache
 	httpServer *http.Server
+	// metrics serves /metrics on its own port; nil when metrics are off.
+	metrics *metrics.Server
 }
 
 // New creates a Server with all services wired up.
@@ -56,6 +60,9 @@ func New(cfg config.Config, q repository.Querier, database Database) (*Server, e
 	s.search = backend.NewSearchCache(s.music.SoundtrackNames)
 	s.sync = backend.NewSyncService(q, cfg.MusicPath, s.afterSync)
 
+	if cfg.MetricsPort > 0 {
+		s.metrics = metrics.NewServer(cfg.MetricsPort)
+	}
 	s.httpServer = &http.Server{
 		Addr:         fmt.Sprintf(":%d", cfg.Port),
 		Handler:      s.RegisterRoutes(),
@@ -111,11 +118,21 @@ func NewServerInstance() *Server {
 	if err != nil {
 		logger.Fatal("Failed to create server", zap.Error(err))
 	}
+	prometheus.MustRegister(metrics.NewPoolCollector(database.Pool))
+	if err := s.sync.UpdateLibraryMetrics(ctx); err != nil {
+		logger.Error("Failed to count the library", zap.Error(err))
+	}
 	return s
 }
 
-// ListenAndServe starts the HTTP server. It returns nil after a graceful shutdown.
+// ListenAndServe starts the HTTP server and the metrics server. It returns nil after a
+// graceful shutdown. The server keeps running without metrics if their port cannot be opened.
 func (s *Server) ListenAndServe() error {
+	if s.metrics != nil {
+		if err := s.metrics.Start(); err != nil {
+			logging.GetLogger().Error("Failed to start the metrics server", zap.Error(err))
+		}
+	}
 	logging.GetLogger().Info("Server starting", zap.String("address", s.httpServer.Addr))
 	if err := s.httpServer.ListenAndServe(); !errors.Is(err, http.ErrServerClosed) {
 		return err
@@ -126,6 +143,9 @@ func (s *Server) ListenAndServe() error {
 // Shutdown stops accepting requests, waits for running requests and then closes the database.
 func (s *Server) Shutdown(ctx context.Context) error {
 	err := s.httpServer.Shutdown(ctx)
+	if s.metrics != nil {
+		err = errors.Join(err, s.metrics.Shutdown(ctx))
+	}
 	s.sync.Wait()
 	s.characters.Close()
 	s.db.Close()