Fix TypeScript compilation errors and update .gitignore

backend/src/modules/messages/messages.resolver.ts

@@ -7,7 +7,7 @@ import { GqlAuthGuard } from '../auth/guards/gql-auth.guard';
 import { CurrentUser } from '../auth/decorators/current-user.decorator';
 import { User } from '../users/entities/user.entity';
 
-const pubSub = new PubSub();
+const pubSub = new PubSub() as any;
 
 @Resolver(() => Message)
 @UseGuards(GqlAuthGuard)

backend/src/modules/users/users.service.ts

@@ -58,7 +58,7 @@ export class UsersService {
   async updateOnlineStatus(id: string, isOnline: boolean): Promise<void> {
     await this.usersRepository.update(id, {
       isOnline,
-      lastSeen: isOnline ? null : new Date(),
+      lastSeen: isOnline ? undefined : new Date(),
     });
   }
 }