* Centralize ball state generation in `BaseMode`
* Track turn count, player, and ball state consistently
* Prevent 8-ball, 9-ball, and colored snooker balls from being marked valid when reaped/sunk
* Update mode initialization and ball-state assignment
* Normalize Free Ball mode node name to `freeball`
* add Free Ball game mode and lobby selection
* refactor base mode ball state tracking for reaped/sunk balls
* add player ownership tracking and colored-ball support
* add initial 9-ball mode implementation
* update 8-ball and snooker modes to use base ball handling
* replicate ball linear velocity for multiplayer synchronization
* improve ball collision sound propagation and physics settings
* reenable game music and initialize game signals
* improve lobby input focus and mode selection behavior
* adjust cue impulse origin and default game mode
