Anyone may join and watch/throw; game auto-starts on first connection.
Ultraworked with [Sisyphus](https://github.com/code-yeongyu/oh-my-openagent)
Co-authored-by: Sisyphus <clio-agent@sisyphuslabs.ai>
Replace std::sync::Mutex with tokio::sync::Mutex; extract try_join_room, register_player, spawn_forwarder, broadcast_room_state, spawn_message_handler, remove_player.
Use Game::process_throw in the message handler.
Ultraworked with [Sisyphus](https://github.com/code-yeongyu/oh-my-openagent)
Co-authored-by: Sisyphus <clio-agent@sisyphuslabs.ai>
