fix(bot): wire aiOpponent into joined and update server messages

packages/server/src/ws.ts

@@ -147,6 +147,7 @@ async function onHello(ctx: SocketCtx, msg: Extract<ClientMessage, { type: 'hell
     mode: game.mode,
     highlightingEnabled: game.highlightingEnabled,
     opponentConnected: !!game.players[color === 'w' ? 'b' : 'w']?.socket,
+    aiOpponent: game.aiOpponent,
   });
 
   // Notify peer that we're connected.
@@ -283,6 +284,7 @@ function sendUpdateTo(
     drawOffer,
     endReason: game.endReason,
     winner: game.winner ?? null,
+    aiOpponent: game.aiOpponent,
   });
 }