Firebase实时数据库规则不适用于新用户

我的Firebase实时数据库有以下规则：

{
  "rules": {
    "users": {
      "$user_id": {
        ".read": "auth !== null && auth.uid == $user_id",
        ".write": "auth !== null && auth.uid == $user_id",
        ".validate": "data.hasChildren(['calculations', 'daily', 'firstName', 'lastName', 'monthly', 'profileImageUrl', 'uid', 'username', 'weekly'])",
        "calculations": {
          ".validate": "data.isNumber()",
        },
        "daily": {
          ".validate": "data.isNumber()",
        },
        "firstName": {
          ".validate": "data.isString()",
        },
        "lastName": {
          ".validate": "data.isString()",
        },
        "monthly": {
          ".validate": "data.isNumber()",
        },
        "profileImageUrl": {
          ".validate": "data.isString()",
        },
        "uid": {
          ".validate": "data.isString()",
        },
        "username": {
          ".validate": "data.isString()",
        },
        "weekly": {
          ".validate": "data.isNumber()",
        },
        "$other": {
          ".validate": false
        }
      }
    }
  }
}

适用于新用户的旧Firebase实时数据库规则：

{
  "rules": {
    ".read": "auth.uid == $user_id",
    ".write": "auth.uid == $user_id"
  }
}

使用电子邮件和密码进行Firebase身份验证：

// Firebase Authentication to create a user with email and password
auth.createUserWithEmailAndPassword(email, password)
    .addOnCompleteListener(this) { task ->
        if (task.isSuccessful) {
            val user = auth.currentUser
            // Send an email verification to the user. Only allow them to login after they
            // have verified their email.
            user!!.sendEmailVerification().addOnCompleteListener { task ->
                if (task.isSuccessful) {
                    // Save username, first name, and last name on Firebase Database
                    val uid = auth.uid ?: ""
                    val ref = database.getReference("/users/$uid")
                    val newUser = User(uid, userName, firstName, lastName, 0.0, 0.0, 0.0, 3, "")
                    ref.setValue(newUser)

                    Toast.makeText(
                        this,
                        "Please check your inbox and verify your email address.",
                    Toast.LENGTH_LONG).show()

                    val intent = Intent(this, LoginActivity::class.java)
                    intent.flags = Intent.FLAG_ACTIVITY_CLEAR_TASK.or(Intent.FLAG_ACTIVITY_NEW_TASK)
                    startActivity(intent)
                }
            }
        }
    }
    // If sign in fails, display a message to the user.
    .addOnFailureListener {
        Toast.makeText(
            baseContext, "Failed to create an account: ${it.message}",
            Toast.LENGTH_LONG
        ).show()
    }

用户类别：

@IgnoreExtraProperties
data class User(
    val uid: String,
    val username: String,
    var firstName: String,
    var lastName: String,
    val daily: Double,
    val weekly: Double,
    val monthly: Double,
    val calculations: Int,
    val profileImageUrl: String
)

这些规则适用于现有用户。但是，如果我尝试创建一个新用户，这些规则将不起作用。我无法在数据库中为已注册的新用户创建新数据。我该如何解决？