Broadcast Chat To Class

Send a chat message to EVERYONE in the class — the main room and all active breakout rooms — regardless of which room the sender is currently in.

Powers the chat scope toggle ("this room" vs "everyone"): normal messages go over the sender's own LiveKit data channel (room-local); this endpoint covers the rest of the class server-side. The sender's OWN room is excluded — their client already published the message locally there (with local echo).

Open to any current participant of the origin room, not just the host — students in a breakout can ask the whole class / reach the teacher too.