Hi,
Configuring database flags requires corresponding roles / permissions. I suggest you contact the Cloud SQL Administrator of the instance to apply for the privilege in order to complete the operation.
Hope it helps!
Hello, RafaelThere are a number of reasons why the error may have been returned. In fact, a similar issue reported in the past was traced to the amount of workloads on the CloudSQL instance at the time. Also, the issue sometimes was found to be transient as there were times observed in the past that restarting the Instance resolves the issue. For better troubleshooting of the issue, which may involve reviewing configurations on your Project, I recommend you contact the GCP Support Engineers[1] or if you think this issue is a bug and you are using the appropriate User account but it is failing, then open an issue using this link[2].
About the flag, hot_standby_feedback, from the information provided on this CloudSQL for Postgres page[3], the flag is actually supported. I did a test on my test environment and I was able to successfully add the flag without any additional access or permission. If you can't change the flag, can you provide information about your experience? Do you have an error reported or the field is grayed out?