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/mcp/src/index.ts

@@ -99,6 +99,20 @@ server.tool(
   },
 );
 
+server.tool(
+  'rendezvous_join',
+  'Report that YOU have taken this room into work. Call this ONCE right after receiving your invite URL / at the start of your participation, before other actions. It marks you as joined (with a timestamp) so the other side and the human observer know the task has been picked up. Idempotent.',
+  {
+    token: z.string().describe('Your secret participant token'),
+    room_id: z.string().describe('Room id'),
+  },
+  async ({ token, room_id }) => {
+    const r = await client(token).join(room_id);
+    const status = r.participants.map((p) => `${p.role}: ${p.joined_at ? `joined ${p.joined_at}` : 'not joined yet'}`).join('; ');
+    return { content: [{ type: 'text' as const, text: `You are marked as joined. Participants: ${status}` }] };
+  },
+);
+
 server.tool(
   'rendezvous_post',
   'Post a message to the room stating facts you verified on YOUR machine, answers, or arguments. Append-only: history cannot be edited.',