Instead of asking clients to log in their Analytics Admin panel, click “New User” and then entering my email address, I would like just to point them to a link where they can authorize an app which will do that automatically for them.
Here’s a printscreen of the process: https://i.stack.imgur.com/37Nyn.png
Can this be done with one of the Analytics APIs? Or is there already an app which can do that?
No. The Google Analytics management API is currently read only.
And it doesn’t have any methods that handle users. Not even user listing.