feat(bot): BotDriver with mutex, retry cap, and dispatch

Wires Brain to Game: init/onStateChange/dispose lifecycle, in-flight
mutex, 5-attempt retry loop with attemptHistory, resign-on-cap. Also
adds Game.aiOpponent? field to state.ts for Task 5.

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

packages/server/src/state.ts

@@ -51,6 +51,7 @@ export interface Game {
   armed: { color: Color; from: Square } | null;
   drawOffer: { from: Color; at: number } | null;
   disconnectAt: { w?: number; b?: number };
+  aiOpponent?: { color: Color; brain: 'casual' | 'recon' };
 }
 
 export const RATE_LIMIT = { capacity: 20, refillPerSec: 10 };