Collaborative whiteboard sync

Design the realtime sync backend for a collaborative whiteboard where each open board is a 'room': users join a board and broadcast cursor moves and shape edits to others in that room. Scale: 2M concurrent users across 500k active boards, edits should propagate within ~100ms, and a user's connection must route to wherever that board's other participants are. Cover room routing across many servers, what you broadcast vs persist, and reconnect.