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/queue.sql

@@ -16,7 +16,7 @@ UPDATE queue SET ended_at = NOW()
 WHERE ended_at IS NULL;
 
 -- 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;
 
 -- name: SetQueueCurrentSong :exec
@@ -27,23 +27,23 @@ WHERE uuid = $1;
 -- Appends the queue's last fetched song and makes it the current song.
 -- Does nothing when no song has been fetched since the last call.
 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;
 
 -- name: ListQueueSongs :many
 -- The song columns are NULL when the song has been removed from the library since.
-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