feat(P5B.T2): GamePayload + games wrappers + winner-detect helpers + tests

Adds conversation_games table type + game_make_move RPC to db-types, GamePayload variant and parseMessagePayload branch to shared/attachments, games.ts with createGame/getGame/makeGameMove wrappers plus pure tttWinningLine/c4WinningCells/c4DropRow/isBoardFull helpers, 11 tests covering all winner helpers, and re-export from chat/index.ts.

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

packages/shared/src/chat/attachments.ts

@@ -88,12 +88,20 @@ export interface WatchTogetherPayload {
   session_id: string;
 }
 
+export interface GamePayload {
+  v: 1;
+  type: 'game';
+  game_id: string;
+  game_type: 'ttt' | 'c4';
+}
+
 export type MessagePayload =
   | TextMessagePayload
   | CallEventPayload
   | PollPayload
   | WhiteboardPayload
-  | WatchTogetherPayload;
+  | WatchTogetherPayload
+  | GamePayload;
 
 export type ParsedMessagePayload =
   | {
@@ -120,6 +128,11 @@ export type ParsedMessagePayload =
   | {
       kind: 'watch_together';
       sessionId: string;
+    }
+  | {
+      kind: 'game';
+      gameId: string;
+      gameType: 'ttt' | 'c4';
     };
 
 export function serializeMessagePayload(payload: MessagePayload): string {
@@ -190,6 +203,12 @@ export function parseMessagePayload(raw: string | null): ParsedMessagePayload {
           : '';
         return { kind: 'watch_together', sessionId: id };
       }
+      if (obj.type === 'game') {
+        const p = obj as Partial<GamePayload>;
+        const id = typeof p.game_id === 'string' && p.game_id.length > 0 ? p.game_id : '';
+        const t = p.game_type === 'ttt' || p.game_type === 'c4' ? p.game_type : 'ttt';
+        return { kind: 'game', gameId: id, gameType: t };
+      }
       const t = obj as TextMessagePayload;
       return {
         kind: 'text',