feat(P5B.T6): composer Spielen button + bubble dispatch + game-picker

Wires mini-game entry points: createGamePayload helper in conversationFeatures.ts (GamePayload import added), game state/handler/picker-dialog/modal-mount/open-event-listener in ConversationPage.tsx (DM-only guard uses conversation.members[].userId camelCase as confirmed), and parsed.kind==='game' bubble branch in MessageBubble.tsx dispatching chatapp:open-game CustomEvent.

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

apps/desktop/src/lib/conversationFeatures.ts

@@ -6,6 +6,7 @@ import {
   type PollOption,
   type WhiteboardPayload,
   type WatchTogetherPayload,
+  type GamePayload,
 } from '@chat-app/shared/chat';
 
 export type AttachmentBucket = 'media' | 'audio' | 'files';
@@ -117,6 +118,16 @@ export function createWatchTogetherPayload(sessionId: string): string {
   return serializeMessagePayload(payload);
 }
 
+export function createGamePayload(gameId: string, gameType: 'ttt' | 'c4'): string {
+  const payload: GamePayload = {
+    v: 1,
+    type: 'game',
+    game_id: gameId,
+    game_type: gameType,
+  };
+  return serializeMessagePayload(payload);
+}
+
 export function summarizePollVotes(
   options: PollOption[],
   reactions: ReactionSummaryInput[],