Of course when I say downgrade I just mean "wiped the drive entirely and installed Mojave from scratch" because it turns out that I had both software and hardware that just didn't work on Big Sur, but now the App Store does not seem to have any way for me to say "forget that I was ever on Big Sur" and I can't install apps I had installed before. Even free apps like The Unarchiver or MS Remote Desktop Client refuse to install and show a little cloud-download icon, with no way to say "please just reset yourself, I'm on Mojave, I need the Mojave versions of everything".

I tried Googling for this, but I can't seem to find a single page (either on the web or even just here) that explains how to actually fix this problem. Lots of pages that explain how to get the old version of MacOS itself through the App Store, lots of articles about getting older versions of iOS apps on older iPhones, but not a single result for how to tell the App Store to forget the "newer" version and instead pull the version appropriate for the OS that the App Store is running in...
Is there a way to do this on a machine without backups made before the erase or upgrade?
diskutilto delete the entire APFS disk, then created two new macos extended/journaled partitions and installed Mojave on one of those, with the other as a data partition. (I did make the mistake of initially forgetting to do that, and was amazed that Mojave didn't tell me it didn't like that until after it finished the full install). It did turn one of those into an APFS container for the Mojave install though, so/dev/disk0has a 500GB APFS container that's mounted as synthesized/dev/disk1, and a regular 3.5TB HFS partition now. – Mike 'Pomax' Kamermans Feb 23 '21 at 02:35