In order to deploy via Cloud Build located in project MANAGEMENT to CloudFunction located in project STAGING,PROD you will need:
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In project MANAGEMENT, get email of account for
xxxxxxxx@cloudbuild.gserviceaccount.com
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In project STAGING and PROD add this account as princial into IAM and add Roles:
IAM Role Name IAM Role Permission Cloud Functions Developer roles/cloudfunctions.developer
Service Account User roles/iam.serviceAccountUser