Add multiplayer room lifecycle and lobby

[halfdimension]

Adds authenticated multiplayer room lifecycle and frontend room lobby.

• Adds backend room APIs for create, join, leave, close, get room, and list my rooms
• Requires JWT auth for room APIs
• Adds host/member model with deterministic host transfer on host leave
• Adds frontend room lobby for creating and joining rooms
• Connects WebSocket presence only after joining/creating a room
• Shows room code, status, members, host badge, online count, leave, and close actions
• Keeps guest solo gameplay unchanged