Sketchup Pro refuses to open browser login page

It’s actually an expression of succes:

Try if deleting the webcache folder helps of SketchUp:
Stop SketchUp, delete the Webcache folder in this location:
%AppData%/SketchUp/SketchUp 2021/SketchUp
Change the standard browser in your system
Or delete all caches related to trimble.
Start SketchUp and sign in.