feat(games): add solo mode to room creation and AU currency betting

Solo mode is now a toggle in the chess room creation modal, available
to all users instead of admin-only. Betting lets players wager AU on
games with preset amounts, async deduction on game start, and automatic
payout/refund on game end.

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

shared/lib/constants.ts

@@ -39,6 +39,8 @@ export enum TransactionType {
     QUEST_REWARD = 'QUEST_REWARD',
     TRIVIA_ENTRY = 'TRIVIA_ENTRY',
     TRIVIA_WIN = 'TRIVIA_WIN',
+    GAME_BET = 'GAME_BET',
+    GAME_WIN = 'GAME_WIN',
 }
 
 export enum ItemTransactionType {