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/queue.sql.go

@@ -13,17 +13,17 @@ import (
 
 const addLastFetchedToQueue = `-- name: AddLastFetchedToQueue :exec
 WITH added AS (
-    INSERT INTO queue_song (queue_uuid, song_no, song_uuid, soundtrack_name, song_name)
+    INSERT INTO queue_song (queue_uuid, song_no, song_uuid, soundtrack_name, song_name, mode)
     SELECT q.uuid,
            (SELECT COALESCE(MAX(qs.song_no), -1) + 1 FROM queue_song qs WHERE qs.queue_uuid = q.uuid),
-           s.uuid, st.soundtrack_name, s.song_name
+           s.uuid, st.soundtrack_name, s.song_name, COALESCE(q.last_fetched_mode, 'unknown')
     FROM queue q
     JOIN song s ON s.uuid = q.last_fetched_song_uuid
     JOIN soundtrack st ON st.id = s.soundtrack_id
     WHERE q.uuid = $1
     RETURNING queue_uuid, song_no
 )
-UPDATE queue SET current_song = added.song_no, last_fetched_song_uuid = NULL
+UPDATE queue SET current_song = added.song_no, last_fetched_song_uuid = NULL, last_fetched_mode = NULL
 FROM added
 WHERE queue.uuid = added.queue_uuid
 `
@@ -37,7 +37,7 @@ func (q *Queries) AddLastFetchedToQueue(ctx context.Context, argUuid uuid.UUID)
 
 const createQueue = `-- name: CreateQueue :one
 INSERT INTO queue DEFAULT VALUES
-RETURNING uuid, current_song, last_fetched_song_uuid, started_at, ended_at
+RETURNING uuid, current_song, last_fetched_song_uuid, last_fetched_mode, started_at, ended_at
 `
 
 func (q *Queries) CreateQueue(ctx context.Context) (Queue, error) {
@@ -47,6 +47,7 @@ func (q *Queries) CreateQueue(ctx context.Context) (Queue, error) {
 		&i.Uuid,
 		&i.CurrentSong,
 		&i.LastFetchedSongUuid,
+		&i.LastFetchedMode,
 		&i.StartedAt,
 		&i.EndedAt,
 	)
@@ -74,7 +75,7 @@ func (q *Queries) EndQueue(ctx context.Context, argUuid uuid.UUID) error {
 }
 
 const getQueue = `-- name: GetQueue :one
-SELECT uuid, current_song, last_fetched_song_uuid, started_at, ended_at
+SELECT uuid, current_song, last_fetched_song_uuid, last_fetched_mode, started_at, ended_at
 FROM queue
 WHERE uuid = $1
 `
@@ -86,6 +87,7 @@ func (q *Queries) GetQueue(ctx context.Context, argUuid uuid.UUID) (Queue, error
 		&i.Uuid,
 		&i.CurrentSong,
 		&i.LastFetchedSongUuid,
+		&i.LastFetchedMode,
 		&i.StartedAt,
 		&i.EndedAt,
 	)
@@ -93,7 +95,7 @@ func (q *Queries) GetQueue(ctx context.Context, argUuid uuid.UUID) (Queue, error
 }
 
 const listQueueSongs = `-- name: ListQueueSongs :many
-SELECT qs.song_no, qs.song_uuid, qs.soundtrack_name, qs.song_name,
+SELECT qs.song_no, qs.song_uuid, qs.soundtrack_name, qs.song_name, qs.mode,
        s.path, s.times_played, s.soundtrack_uuid
 FROM queue_song qs
 LEFT JOIN song s ON s.uuid = qs.song_uuid
@@ -106,6 +108,7 @@ type ListQueueSongsRow struct {
 	SongUuid       uuid.UUID `json:"song_uuid"`
 	SoundtrackName string    `json:"soundtrack_name"`
 	SongName       string    `json:"song_name"`
+	Mode           string    `json:"mode"`
 	Path           *string   `json:"path"`
 	TimesPlayed    *int32    `json:"times_played"`
 	SoundtrackUuid uuid.UUID `json:"soundtrack_uuid"`
@@ -126,6 +129,7 @@ func (q *Queries) ListQueueSongs(ctx context.Context, queueUuid uuid.UUID) ([]Li
 			&i.SongUuid,
 			&i.SoundtrackName,
 			&i.SongName,
+			&i.Mode,
 			&i.Path,
 			&i.TimesPlayed,
 			&i.SoundtrackUuid,
@@ -156,16 +160,17 @@ func (q *Queries) SetQueueCurrentSong(ctx context.Context, arg SetQueueCurrentSo
 }
 
 const setQueueLastFetched = `-- name: SetQueueLastFetched :exec
-UPDATE queue SET last_fetched_song_uuid = $2
+UPDATE queue SET last_fetched_song_uuid = $2, last_fetched_mode = $3
 WHERE uuid = $1
 `
 
 type SetQueueLastFetchedParams struct {
 	Uuid                uuid.UUID `json:"uuid"`
 	LastFetchedSongUuid uuid.UUID `json:"last_fetched_song_uuid"`
+	LastFetchedMode     *string   `json:"last_fetched_mode"`
 }
 
 func (q *Queries) SetQueueLastFetched(ctx context.Context, arg SetQueueLastFetchedParams) error {
-	_, err := q.db.Exec(ctx, setQueueLastFetched, arg.Uuid, arg.LastFetchedSongUuid)
+	_, err := q.db.Exec(ctx, setQueueLastFetched, arg.Uuid, arg.LastFetchedSongUuid, arg.LastFetchedMode)
 	return err
 }