Multiplayer room state and broadcast

Design the room/session backend for a real-time multiplayer collaborative or game app where state is room-scoped (a game match, a whiteboard, a watch-party). Each room has an authoritative live state mutated by member actions and broadcast to all members. Scale: 1M concurrent rooms, up to 1,000 members in the largest rooms, sub-150ms action-to-broadcast. Rooms are created/destroyed constantly; a room's host node can crash.