feat: MusicBrainz BPM enrichment + improved AI prompts

- lookupRecordingWithTags, extractBpmFromTags, extractTimeSigFromTags, getMusicBrainzRecording added to MB client
- upsertSong preserves existing BPM via COALESCE on conflict
- updateSongBpm helper for async enrichment writes
- AnalysisInput gains confirmedBpm / confirmedTimeSigNum fields
- POST /api/analyze fetches confirmed BPM from DB then MB tags before generation
- All three AI providers use confirmedBpm as authoritative and build enriched userMessage
- POST /api/tracks auto-registration now fetches tags via getMusicBrainzRecording
- Updated User-Agent and MB client fallback URL to Gitea

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

lib/db/client.ts

@@ -92,8 +92,8 @@ export async function upsertSong(song: Omit<SongRow, "created_at" | "updated_at"
        title = EXCLUDED.title,
        artist = EXCLUDED.artist,
        duration_seconds = EXCLUDED.duration_seconds,
-       acousticbrainz_bpm = EXCLUDED.acousticbrainz_bpm,
-       acousticbrainz_time_sig_num = EXCLUDED.acousticbrainz_time_sig_num,
+       acousticbrainz_bpm = COALESCE(EXCLUDED.acousticbrainz_bpm, songs.acousticbrainz_bpm),
+       acousticbrainz_time_sig_num = COALESCE(EXCLUDED.acousticbrainz_time_sig_num, songs.acousticbrainz_time_sig_num),
        source = EXCLUDED.source`,
     [
       song.mbid,
@@ -107,6 +107,26 @@ export async function upsertSong(song: Omit<SongRow, "created_at" | "updated_at"
   );
 }
 
+/**
+ * Updates only the BPM and time-signature fields of a song row.
+ * No-ops if the song doesn't exist.
+ * Used by the async MusicBrainz tag enrichment path.
+ */
+export async function updateSongBpm(
+  mbid: string,
+  bpm: number | null,
+  timeSigNum: number | null
+): Promise<void> {
+  await query(
+    `UPDATE songs
+     SET acousticbrainz_bpm = COALESCE($2, acousticbrainz_bpm),
+         acousticbrainz_time_sig_num = COALESCE($3, acousticbrainz_time_sig_num),
+         updated_at = NOW()
+     WHERE mbid = $1`,
+    [mbid, bpm, timeSigNum]
+  );
+}
+
 // ─── Tempo map queries ────────────────────────────────────────────────────────
 
 export interface TempoMapRow {