One mechanism to ensure that nobody can take the COPY_ONLY backup of your database is to use Transparent Data Encryption that automatically encrypts all backups. In that case you would need to use Customer-managed (BYOK) TDE where you will keep your encryption key in Azure Key-Vault. User-initiated COPY_ONLY backups are (currently) not allowed if you are using Service-managed TDE.
If you don’t use TDE on the database or there is a risk that someone can remove TDE from database and then take a backup, Managed Instance provides auditing mechanism that enables you to track who performed a backup and when. This way you can always track if some unauthorized action is happening.
Read on for the solution. Looking through it, it seems like conceptually it’d work equally well with on-prem/IaaS SQL Server as with Managed Instances.