You have misunderstood the requirements of the GDPR. CNIL, for example, has made it explicitly clear that so long as an effective retention policy is in place then PII does not need to be removed from backups on demand.
Well that's just a crock. You simply have to have a policy that says how long you retain backups for, and what you would do if you needed to delete PI if required to do so under GDPR.