As @Greg said, we looked into this and it seems that it may be a issue with SketchUp 2021 Version 21.0.339.
The version of the Chromium browser that ships with that particular version of SketchUp 2021 may have a bug that prevents out login code from working correctly.
If possible, upgrading to the latest version of SketchUp should solve the issue. If you need to stay with SketchUp 2021, you can simply update to the latest version of 2021, which as of today, 7/2/2024, is Version 21.1.332.
I found this unofficial link where you can download older SketchUp versions, and it currently includes version 21.1.332:
https://www.sketchup3d.de/download/center/#199-217-version-2021-archiv
That said, we are currently looking to see if we can figure out a workaround. If we do, we’ll release an updated installer and post about it here!
Thanks everyone for letting us know about this issue, hopefully we can get it resolved soon!