But, the backwards compatibility problem I referred to remains: should I not be able to quit MC22, start MC21, and have MC21 load the library I've been using for a long time?
The upgrade from MC21 to MC22 involved a library format change that is not backward compatible. This is the first time this has happened since I have been using MC, back at version 18. If the library format does need to be changed at any time, it is always done at a major release upgrade. i.e. MC21 to MC22.
When you installed MC22 (at least for the Windows version), the installation process should have found the MC21 library, moved it to a new MC22 specific location, and updated it to the MC22 format. If you try to open a MC21 library in MC22 it should also be updated. If you then tried to open the same library with MC21, it shouldn't work.
If the MC22 installation process didn't find the MC21 library, you would have needed to restore an MC21 library backup into MC22, at which time the library format would have been converted.
All of this is why the Library is in a folder that is specific to the major release. If you moved the library to a non-major release specific folder, I would expect the installation process to still try to keep the two version separate. If it didn't, and just updated the library in situ, then you don't have a MC21 library any more, except in backups.
You can run two versions on a PC/Mac, but not at the same time. In general though, it isn't a good idea. For example, on Windows, if you are using MC22, close it, and then open MC21, MC21 will register some of its components with Windows in order to work properly. When you go back to MC22, it will in turn re-register its components. Regardless, you will have to use two separate libraries, and not the same one.
Note that I am using the Windows version of MC, and haven't checked what the OSX version does with the library. I would expect it to be similar though.