feat(02-02): wire WebSocket broadcast loop and command dispatch

- Add broadcast_loop sending position ticks at 10Hz to all clients
- Replace echo stub with play/pause/seek/load command dispatch to MPVEngine
- Start broadcast_loop as asyncio task in lifespan, cancel on shutdown
- Use get_engine callable to avoid circular import at module level

lightsync/api/ws.py

@@ -1,3 +1,4 @@
+import asyncio
 import json
 from fastapi import APIRouter, WebSocket, WebSocketDisconnect
 
@@ -31,6 +32,20 @@ class ConnectionManager:
 manager = ConnectionManager()
 
 
+async def broadcast_loop(get_engine) -> None:
+    """Broadcast playback state to all WebSocket clients at 10Hz (AUD-04).
+
+    Args:
+        get_engine: callable returning the MPVEngine instance (avoids import cycle)
+    """
+    while True:
+        await asyncio.sleep(0.1)
+        engine = get_engine()
+        if engine and manager.active_connections:
+            state = engine.get_state()
+            await manager.broadcast({"type": "tick", **state})
+
+
 @router.websocket("/ws")
 async def websocket_endpoint(websocket: WebSocket):
     await manager.connect(websocket)
@@ -38,8 +53,33 @@ async def websocket_endpoint(websocket: WebSocket):
         while True:
             data = await websocket.receive_text()
             msg = json.loads(data)
-            # Phase 2 will dispatch msg["type"] to handlers
-            # For now: echo back with type=ack
-            await websocket.send_text(json.dumps({"type": "ack", "echo": msg}))
+            msg_type = msg.get("type")
+
+            # Import engine reference from main (module-level var)
+            from lightsync.main import engine
+
+            if engine is None:
+                await websocket.send_text(json.dumps({"type": "error", "message": "engine not ready"}))
+                continue
+
+            if msg_type == "play":
+                engine.play()
+                await websocket.send_text(json.dumps({"type": "ack", "command": "play"}))
+            elif msg_type == "pause":
+                engine.pause()
+                await websocket.send_text(json.dumps({"type": "ack", "command": "pause"}))
+            elif msg_type == "seek":
+                position = float(msg.get("position", 0))
+                engine.seek(position)
+                await websocket.send_text(json.dumps({"type": "ack", "command": "seek", "position": position}))
+            elif msg_type == "load":
+                path = msg.get("path", "")
+                if path:
+                    engine.load(path)
+                    await websocket.send_text(json.dumps({"type": "ack", "command": "load", "path": path}))
+                else:
+                    await websocket.send_text(json.dumps({"type": "error", "message": "missing path"}))
+            else:
+                await websocket.send_text(json.dumps({"type": "ack", "echo": msg}))
     except WebSocketDisconnect:
         manager.disconnect(websocket)

lightsync/main.py

@@ -1,3 +1,4 @@
+import asyncio
 import os
 from contextlib import asynccontextmanager
 from pathlib import Path
@@ -27,8 +28,15 @@ async def lifespan(app: FastAPI):
     engine = MPVEngine(ao=ao)
     engine.start()
     app.state.engine = engine
+    from lightsync.api.ws import broadcast_loop
+    task = asyncio.create_task(broadcast_loop(lambda: engine))
     yield
     # Shutdown
+    task.cancel()
+    try:
+        await task
+    except asyncio.CancelledError:
+        pass
     engine.stop()
     await registry.save()