Hi!
There are 2 kinds of backups, Manual and Automatic. They both save a binlog.
If you have Automatic backups, they are kept for 7 days and the binlog is deleted automatically with the backup after 7 days.
If you have manual backups, the binlogs and backups will not be deleted.
It is suggested to use automated backups as Cloud SQL will manage your backups and deletes. This has been confirmed with the engineering team[1].