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/backend/library_integration_test.go

@@ -29,6 +29,11 @@ func TestLibraryAndStatisticsWithPostgres(t *testing.T) {
 	s.Wait()
 	require.Empty(t, s.Result().CatchedErrors)
 
+	count, err := q.CountLibrary(ctx)
+	require.NoError(t, err)
+	assert.Equal(t, int64(4), count.Soundtracks)
+	require.NoError(t, s.UpdateLibraryMetrics(ctx))
+
 	library := NewLibraryService(q)
 	soundtracks, err := library.Soundtracks(ctx)
 	require.NoError(t, err)