Yes, that works. Just install some KDE plasma desktop metapackage of your choice and, if you like, you can remove cinnamon and related GTK packages afterwards by removing libgtk.

desktop interfaces like cinnamon and plasma run on top of the actual OS

Yes, I would call the rest "base OS" which is also how the things are often called. As the Desktop contains tons of things that "operate" ;)

it's possible to swap them without having to reinstall

Yes, and no.

On Linux Distros everything is in a package. For example a package for Firefox.

Packages can be put into groups, and packages can have dependencies. For example I install Firefox and it will also pull in the language packs.

You could install a desktop by installing the group "KDE Plasma Desktop" or how it is called. Or there may be a package "kde-plasma-meta" (like on Arch) that doesnt contain anything but in its description has the list of packages it "requires" so these will automatically be installed.

The same way you can also uninstall your old desktop.

But the question is: what about configurations, and what does Linux Mint do here?

Linux mint is just Ubuntu, now also Debian, with the Cinnamon Desktop, some Mint-specific apps and a theme and custom settings.

These customizations are the reason why you would install Mint instead of Ubuntu Cinnamon.

(Also of course the fact that people dont know how distros work)

Now Desktop environments have different icons and apps, but may use the same method to define "this is the standard I use".

I.e. If you install KDE Plasma it may mess up your icons on Mint.

Packages have configurations and following the Unix philosophy "everything is a file", these configs are stored in config files.

The default ones are in /etc while your own ones (which confusingly also include tons of stuff you didnt manually change) are in ~/.config so your home directory.

Different users on Linux have different home directories.

So if you just want to test a DE, you should create a different user and only use that DE with that user.

The issue is that these config files are not managed, at all. If you uninstall a package (or many, like the Cinnamon Desktop), the configs will stay there.

So even if you do it cleanly, uninstall the DE, only have a Terminal interface (TTY) left and install the new one, you may have conflicts.

That sucks a lot and I dont know a fix for it. Distros should put all their configs in something like ~/.config/kde (there is a feature request).

This is why installing different desktops is always messy. Poorly.

Atomic Distros like Fedora Kinoite also dont change that.