I need to register a folder of a drive of the machine that ArcGIS Pro runs on, and one on a network path.
For both I get "Error validating with server".
What works is registering SDE's and the root of the drive of the machine (D:\).
I'm not sure if this will answer your question, but I think the information you need is in the following documentation:
You may also need to ensure that the Windows service account that is running the ArcGIS Server application has, at minimum, read and write access to the directories that you are trying to register.
Hope that helps.
Is your server federated with a portal or stand alone? The methods differ depending on this.
In either case, the "Run As" account for server must have, at a minimum, read access to the date store you are registering.