Hey Daedalus,
Looking at the error, it appears the user account in which you are logging in with does not have READ access to the Custom API table.
This table was introduced in newer versions of the Dataverse.
In order to rectify the issue, you will have to either adjust the security role(s) for your particular user so that it has READ access to the Custom API table or add a role to that user record that already has the proper access, such as System Administrator.
If you already have the System Administrator security role added then this is a larger issue, but my thought would be you do not and the options above should solve your problem.
For your knowledge, based on the error message, this line gives us the issue at hand:
Principal user (Id=0ba7d097-96ab-ec11-983f-0022480b6c03, type=8, roleCount=5, privilegeCount=1016, accessMode=0), is missing prvReadCustomAPI privilege.
The orange highlighted area is the GUID of the User record in the system, and the green highlighted is the name of the privilege that the user is missing (prvReadCustomAPI = Read Privilege for the Custom API table).
Adding READ permission to this table for this user may still give you an error if there are other missing permissions, so understanding the line above will help you hopefully add all of the required permissions in order to connect to the Plugin Registration Tool.
If you have any more questions don't hesitate to ask!
Thanks!
Matt Bayes