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/queries/statistics.sql

@@ -207,3 +207,9 @@ LEFT JOIN song s ON g.id = s.soundtrack_id
 WHERE g.deleted IS NULL
 GROUP BY g.id, g.soundtrack_name, g.times_played, g.last_played
 ORDER BY g.soundtrack_name;
+
+-- name: CountLibrary :one
+-- Soundtracks and songs in the library, without deleted soundtracks.
+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;