Support have done a lot of testing, and I also went back to test more. In both our cases we kept trying things, and that would seem to fix the problem. After my last tests though it seems to be that it either will work or it won’t work, and what actions I took don’t affect that. You can imagine that it can take a long time to get to that conclusion, if for most of the testing you think you just did something relevant!
So, what you have found seems to be the case, and that closing and reopening SketchUp without doing anything different, will leave you good for the rest of that session, or bad.
After I realized that my actions were not affecting anything, I was able to work with a developer to try different ideas, and there is good hope that we know how to fix it. Can’t tell you exactly when that might appear as an update.
Meanwhile, now that we think we know what is really going wrong I am trying to figure out a work around, that you could do in existing 2021 and 2022 versions.