Ah yes I forgot the part about it being AD groups, sorry. It would seem that the LDAP plugin may need to be extended then to do that.

I recently worked with another integration where they had the same need as I alluded to before, and they ended up taking the approach to generate the user.csv for HR Import based on custom export from AD. On that note, a sort of hacky solution would be to use a custom PHP script that uses the LDAP settings to query the AD and generate the HR Sync import file from AD manually, and in doing so you could build logic into that to populate custom user fields. If you're going that far then you could also integrate it with hierarchies I suppose.

The LDAP sync, by default, occurs when user logs in. There is also a separate LDAP sync cli script that can be custom scheduled to run periodically, kind of like HR Import/Totara Sync.