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/db/repository/models.go

@@ -15,6 +15,7 @@ type Queue struct {
 	Uuid                uuid.UUID          `json:"uuid"`
 	CurrentSong         int32              `json:"current_song"`
 	LastFetchedSongUuid uuid.UUID          `json:"last_fetched_song_uuid"`
+	LastFetchedMode     *string            `json:"last_fetched_mode"`
 	StartedAt           pgtype.Timestamptz `json:"started_at"`
 	EndedAt             pgtype.Timestamptz `json:"ended_at"`
 }
@@ -25,6 +26,7 @@ type QueueSong struct {
 	SongUuid       uuid.UUID          `json:"song_uuid"`
 	SoundtrackName string             `json:"soundtrack_name"`
 	SongName       string             `json:"song_name"`
+	Mode           string             `json:"mode"`
 	AddedAt        pgtype.Timestamptz `json:"added_at"`
 }