Default Backup to be Copy-Only
Not really an answer - it's not possible to do it.

2 work arounds that we considered:


Creating a Stored Proc/SQL Agent Job that could be executed by the user that did the backup
Convince the business that they can trust us to do their backups for them


We went with option #2, and scheduled a copy-only backup to run every week on payroll day, and also at the end of the financial year. We told them that we can also run the backup whenever they ask us to do it. We also demonstrated that we can restore any database up to the minute based on our RPO. It made some people in HR disappointed, but the manager signed off on it.

We also disabled their access to backup to prevent any accidents.