If I had to build something like this where I knew I would never edit or manage field groups on the production site I would build a function that would do the checking and deleting as I mentioned above.
Another option might be, instead of deleting groups to mark them as inactive so that they will not be used, this would allow syncing.
Generally, I never delete a field group once I’ve created it.
To be honest, if I had a production site that will only use active JSON files then the field groups of that site would never be stored in the database and the only place the field groups would exist would be in the acf-json folder. I would delete all of the field groups from ACF admin and upload the acf-json folder and just let ACF use the field groups from there. However, this will not work if you’re also syncing the DB in some way.
