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/statistics.sql.go

@@ -12,6 +12,25 @@ import (
 	"github.com/google/uuid"
 )
 
+const countLibrary = `-- name: CountLibrary :one
+SELECT
+    (SELECT COUNT(*) FROM soundtrack WHERE deleted IS NULL) AS soundtracks,
+    (SELECT COUNT(*) FROM song s JOIN soundtrack st ON st.id = s.soundtrack_id WHERE st.deleted IS NULL) AS songs
+`
+
+type CountLibraryRow struct {
+	Soundtracks int64 `json:"soundtracks"`
+	Songs       int64 `json:"songs"`
+}
+
+// Soundtracks and songs in the library, without deleted soundtracks.
+func (q *Queries) CountLibrary(ctx context.Context) (CountLibraryRow, error) {
+	row := q.db.QueryRow(ctx, countLibrary)
+	var i CountLibraryRow
+	err := row.Scan(&i.Soundtracks, &i.Songs)
+	return i, err
+}
+
 const getAllSoundtracksWithSongs = `-- name: GetAllSoundtracksWithSongs :many
 SELECT 
     g.id as soundtrack_id,