feat: add heartbeat/ping to terminal WebSocket

- Backend: Send ping every 30s from WebSocket endpoint
- Frontend: Respond to pings with pongs, detect missed pings (60s timeout)
- Update type definitions to include 'resetting' status

Refs: persistent-terminal-sessions task 6.4

apps/api/src/api/terminal.py

@@ -86,13 +86,14 @@ async def terminal_websocket(
         # Send connected status
         await websocket.send_json({"type": "status", "status": "connected"})
 
-        # Start I/O loops
+        # Start I/O loops and heartbeat
         read_task = asyncio.create_task(_read_loop(session, websocket))
         write_task = asyncio.create_task(_write_loop(session, websocket))
+        heartbeat_task = asyncio.create_task(_heartbeat_loop(websocket))
 
         # Wait for either task to complete (indicating disconnect or error)
         done, pending = await asyncio.wait(
-            [read_task, write_task],
+            [read_task, write_task, heartbeat_task],
             return_when=asyncio.FIRST_COMPLETED,
         )
         
@@ -181,6 +182,20 @@ async def _write_loop(session, websocket) -> None:
         pass
 
 
+async def _heartbeat_loop(websocket: WebSocket) -> None:
+    """Send periodic ping messages to detect disconnections."""
+    try:
+        while True:
+            await asyncio.sleep(30)  # Ping every 30 seconds
+            try:
+                await websocket.send_json({"type": "ping"})
+            except Exception:
+                # WebSocket is closed or broken
+                break
+    except Exception:
+        pass
+
+
 @router.post(
     "/projects/{project_id}/repositories/{repo_id}/instances/{instance_id}/terminal/reset",
     summary="Reset terminal session",