Much worse is that sometimes (once a month?) during this process macOS completely messed up all my open windows: they are all resized to a tiny size. And I have dozens or hundred of them open. This is horribly annoying, and didn’t happen to me before (in 10.11; I skipped 10.12 and 10.13, for reasons similar to the OP. Before that, I went from 10.8 to 10.11; before that, I never missed a release, often was running beta of the OS etc.; but starting with 10.9, too many issues made this undesirable).
I dread switching to 10.15; unfortunately, I will get a new MBP 16” from work, which normally I’d relish, except that there seems to be no way to use it with anything but 10.15. I’ll see if I can delay it until 10.16 is out and will pray that they started to prioritize bug fixes again, but I have little hope that’ll actually happen.
I've previously had these problems, and they were made dramatically worse on Catalina. Each monitor has about 50% chance of correctly loading in, on what used to be 90%. My USB mouse (which is plugged in to the displayport monitor) also loads the incorrect drivers until I unplug and replug it.
--- Well I take that back. It's been updated since last i used it a few years ago. There is display orientation savings now. It might now solve the problem, but it sure looks to make the fix much easier and faster. Trying it now. Thanks
Another option is to use the left side ports at work and the right side at home.