test(runtime-host): include background activity in WebSocket catalogs

Update remote catalog assertions for the Host-owned idle projection on created and renamed Sessions.

Generated-by: Codex

Author: chinawch007

packages/runtime-host/src/__tests__/authenticated-websocket.test.ts

@@ -284,7 +284,11 @@ test('one Local IPC owner and one authenticated WebSocket Client control the sam
       }),
       {
         kind: 'session',
-        session: { ...created, liveRunState: KNOWN_EMPTY_LIVE_RUN_STATE },
+        session: {
+          ...created,
+          liveRunState: KNOWN_EMPTY_LIVE_RUN_STATE,
+          backgroundActivity: 'idle',
+        },
       },
     );
 
@@ -306,7 +310,11 @@ test('one Local IPC owner and one authenticated WebSocket Client control the sam
       renamed.kind === 'committed'
         ? {
             kind: 'session',
-            session: { ...renamed.session, liveRunState: KNOWN_EMPTY_LIVE_RUN_STATE },
+            session: {
+              ...renamed.session,
+              liveRunState: KNOWN_EMPTY_LIVE_RUN_STATE,
+              backgroundActivity: 'idle',
+            },
           }
         : assert.fail('Remote Session rename did not commit'),
     );