Well I found what I needed in the documentation.

https://graphdb.ontotext.com/documentation/10.8/access-control.html#basic-authentication

It looks like the REST API methods support Basic authentication as well as GDB, so I could just log in the same way that I do in other systems. I still don't know what I would do if I was forced to use GDB authentication, but I'm happy that it works using methods that I know.