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/components/MessageBubble.tsx

@@ -442,6 +442,32 @@ export function MessageBubble({
                   defaultValue: 'Nachricht nicht lesbar',
                 })}
               </span>
+            ) : parsed.kind === 'game' ? (
+              <div className="flex items-center gap-3 rounded-2xl border border-accent/30 bg-accent/5 px-4 py-3">
+                <div className="flex h-10 w-10 shrink-0 items-center justify-center rounded-lg bg-accent/20 text-accent">
+                  <svg viewBox="0 0 24 24" fill="none" stroke="currentColor" strokeWidth={2}
+                       strokeLinecap="round" strokeLinejoin="round" className="h-5 w-5">
+                    <rect x="3" y="6" width="18" height="12" rx="3" />
+                    <path d="M8 12h4M10 10v4M16 11v.01M16 14v.01" />
+                  </svg>
+                </div>
+                <div className="min-w-0 flex-1">
+                  <div className="text-sm font-semibold text-fg">{parsed.gameType === 'c4' ? 'Vier-Gewinnt' : 'Tic-Tac-Toe'}</div>
+                  <div className="text-xs text-fg-muted">Gemeinsam spielen</div>
+                </div>
+                <button
+                  type="button"
+                  onClick={() => {
+                    window.dispatchEvent(
+                      new CustomEvent('chatapp:open-game', { detail: { id: parsed.gameId } }),
+                    );
+                  }}
+                  disabled={!parsed.gameId}
+                  className="cursor-pointer rounded-md bg-accent px-3 py-1.5 text-xs font-semibold text-accent-fg transition hover:bg-accent/90 disabled:cursor-not-allowed disabled:opacity-50"
+                >
+                  Spielen
+                </button>
+              </div>
             ) : parsed.kind === 'watch_together' ? (
               <div className="flex items-center gap-3 rounded-2xl border border-accent/30 bg-accent/5 px-4 py-3">
                 <div className="flex h-10 w-10 shrink-0 items-center justify-center rounded-lg bg-accent/20 text-accent">