如何将firebase项目的auth用于其他项目的Firestore？

Question

firestore项目的规则如下

rules_version = '2';
service cloud.firestore {
  match /databases/{database}/documents {
    match /{document=**} {
      allow read, write: if false;
    }
  }
}

之前，我通过firebase函数使用firebase admin sdk来获得对firestore项目的完整控制。

当规则如下所示时，是否可以在客户端对firestore使用auth

rules_version = '2';
service cloud.firestore {
  match /databases/{database}/documents {
    match /{document=**} {
      allow read, write: if request.auth != null;;
    }
  }
}

if (!this.auth && !_auth) {
      this.authApp = firebase.initializeApp(Env.FirebaseAuthConfig, 'auth')
      this.auth = this.authApp.auth()
    }

    if (!this.firestore && !_firestore) {
      this.firestoreApp = firebase.initializeApp(Env.FirebaseFirestoreConfig, 'firestore')
      this.firestoreApp.auth(this.authApp)
      this.firestore = this.firestoreApp.firestore()
    }

但是FirebaseError：请求时权限丢失或不足

请给我一些建议