music: re-enable background loop (default = playful) + profile on/off; coins 2000

- sound.ts: restored startMusic (was a no-op stub) playing the selected track
  through musicGain (in-game mute still applies); default track switched to
  "playful" (per user). Music auto-starts on init when enabled.
- Profile → Audio: re-added a music on/off toggle (so players can disable it
  outside the game too); SFX toggle unchanged.
- Economy tune: starting coins 1000 → 2000 (mock defaultProfile + server
  ProfileDto) so new players start a bit richer.

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

src/lib/sound.ts

@@ -38,7 +38,7 @@ class SoundManager {
   sfxEnabled = loadBool(LS_SFX);
   musicEnabled = loadBool(LS_MUSIC);
   musicTrack: MusicTrack =
-    (typeof window !== "undefined" && (localStorage.getItem(LS_TRACK) as MusicTrack)) || "santoor";
+    (typeof window !== "undefined" && (localStorage.getItem(LS_TRACK) as MusicTrack)) || "playful";
 
   /** Must be called from a user gesture to unlock audio. */
   init() {
@@ -210,8 +210,35 @@ class SoundManager {
     },
   };
 
-  /** Background music was removed from the game — these are inert no-ops. */
-  startMusic() {}
+  /** Start the ambient loop for the current track (plays through musicGain so
+   *  the in-game mute / music volume apply). Idempotent + needs an unlocked ctx. */
+  startMusic() {
+    if (!this.musicEnabled || this.musicTimer || !this.ctx || !this.musicGain) return;
+    const tick = () => {
+      if (!this.ctx || !this.musicGain) return;
+      const cfg = this.TRACKS[this.musicTrack];
+      const now = this.ctx.currentTime;
+      const freq = cfg.notes[this.step % cfg.notes.length];
+      this.step++;
+      const voice = (f: number, scale = 1) => {
+        const osc = this.ctx!.createOscillator();
+        const g = this.ctx!.createGain();
+        osc.type = cfg.type;
+        osc.frequency.value = f;
+        g.gain.setValueAtTime(0.0001, now);
+        g.gain.linearRampToValueAtTime(cfg.peak * scale, now + cfg.attack);
+        g.gain.exponentialRampToValueAtTime(0.0001, now + cfg.dur);
+        osc.connect(g);
+        g.connect(this.musicGain!);
+        osc.start(now);
+        osc.stop(now + cfg.dur + 0.05);
+      };
+      voice(freq);
+      if (cfg.fifth) voice(freq * 1.5, 0.45); // soft fifth above
+    };
+    tick();
+    this.musicTimer = setInterval(tick, this.TRACKS[this.musicTrack].gap);
+  }
 
   stopMusic() {
     if (this.musicTimer) {