- chatHub broadcasts room danmaku over SSE; new subscribers replay the
last N messages on join so they don't face an empty room.
- Add a host-only external push endpoint POST /api/room/{room}/broadcast
(requires room:publish, Bearer token) that marks messages host:true.
- Slide-window rate limiter (room+sender+IP, 5 per 3s) guards both the
public chat and the broadcast endpoint.
- Wire RBAC room:chat policy, SPA routing and the room-creation route.
