Revit 2020.2 release made a change to the Project Base Point that affected many users by removing the clip/unclip capability for it. Previous releases of Revit had a paper clip symbol that the user could see next to the Project Base Point symbol as shown below.
While this clip feature is no longer part of Revit as of the 2020.2 (it is still in 2020.1), the user still has the capability to move the project.
To move/relocate the project, go to the Manage tab -> Project Location panel -> Position dropdown -> Relocate Project. This is in essence the Move command and allows you to move the project to the correct coordinate location. To move the project vertically, go to an elevation or section view.
With the paper clip feature, when you dragged the Project Base Point symbol, the coordinates changed on the screen. You could also type the coordinates directly into the Project Base Point on the screen. It no longer works this way. This did not truly move/relocate the project and actually just provided a local coordinate system that a spot coordinate could report on.
While a user may agree or disagree with this move by Autodesk, it has been changed and users will need to adapt to not having the clip feature for the Project Base Point.
Note that the clip/unclip feature remains the same for the Survey Point and is unchanged.
Applying Technology to Architecture 
This is kinda weird. The paperclip sure enough served a purpose. When moving the basepoint with the clip enabled, the whole model would move too. With the clip disabled, moving the basepoint just moved the basepoint, leaving the model in it’s place. It seems like this new behaviour, it’s no longer possible to move the basepoint without moving the model? A very UNwelcome modification….
@Simon Weel so i just saw this and started trying things out, and it seems that now the default (and only) behavior of the project base point is unclipped, but when using the relocate project tool, it relocates the project base point along with it as if it is clipped. So the project base point becomes a way to create a local control point for levels and elevations that can be moved along with the project and relocated independently based on project needs. I don’t mind this to be honest. The survey point can still be unclipped, which to me makes no sense, i don’t know of a use for that, if i were to ever move the survey point it would be clipped in order to move the 0,0 to a predefined benchmark from a survey, and the internal origin, which is no longer invisible, is the origin for linking other disciplines and for shared sites.