It's been a couple of days and I managed to fix all the issues (for now) on my end and finish the book. I'm not sure what did it exactly, but I made sure to note down all my steps.
Keep in mind that before this, I already cleared user data and reinstalled AP several times, as well as made sure Windows and all my drivers were up to date.
Clear User Data (On Windows, hold control when starting AP and keep holding it until the software has opened, make sure everything is cleared)
Uninstall Affinity Publisher
Reinstall Affinity Publisher (2.2.1, via MSIX installer)
Clear User Data again (make sure that ALL boxes are checked and EVERYTHING is cleared)
Open AP, enter your credentials.
Presto. Ever since I did this, I've had no crashes or authentication issues.