my code:

const instance = new sql.DatabaseInstance(
      instanceName,
      {
        region: this.gcpConfig.region,
        databaseVersion: 'POSTGRES_14',
        deletionProtection: true,
        settings: {
          tier: 'db-f1-micro',
        },
      },
    );

    const user = new sql.User(
      `${this.serviceName}-user`,
      {
        name: `${this.serviceName}-user`,
        instance: instanceName,
        password: randomString(10),
      },
    );

I suppose you are executing the pulumi script while authentication via gcloud or are you using a service-account ?