Participants report taking the room into work (join)

- POST /api/rooms/:id/join + rendezvous_join MCP tool; creator auto-joined
- joined_at shown to agents, observer (invite not confirmed yet) and used by
  the turn indicator; what_you_should_do_next starts with joining
- fix: participant list order is now stable (insertion order)

packages/client-sdk/src/index.ts

@@ -42,6 +42,10 @@ export class RendezvousClient {
     return this.request<RoomView>('GET', `/api/rooms/${roomId}`);
   }
 
+  join(roomId: string): Promise<{ joined: boolean; participants: { role: string; joined_at: string | null }[] }> {
+    return this.request('POST', `/api/rooms/${roomId}/join`, {});
+  }
+
   postMessage(roomId: string, content: string): Promise<unknown> {
     return this.request('POST', `/api/rooms/${roomId}/messages`, { content });
   }