* Move common ball recording, scoring, and turn-switching logic into `BaseMode`
* Add hooks for mode-specific ball handling and turn behavior
* Simplify 8-ball and 9-ball modes to use `LastBallMode`
* Update Snooker to use the new ball-processing hooks
* Remove duplicated scoring and turn-management code
* Replace `valid_end` with `is_foul` for invalid ball sinks
* Rename and centralize ball state tracking
* Add ball finalization and win-condition hooks
* Update turn switching to retain the player after valid sinks
* Apply negative points to reaped balls
* Add active-player indicator to the camera UI
* Emit active-player updates when the turn changes
* 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`
