I click on my desktop and make the finder active.
I right-click (or file) get-info and get info on the desktop.
Under the General Drop-down, Kind is Anything
Further down Open With displays BBEdit.App
A regular folder, Desktop included, has Kind: Folder, and, you are right, no Open With is displayed.
If i open up a list of files under my userid, Desktop is there, and the Kind is listed as Anything.
I wouldn't really care except I can not create files of any kind including folders, nor move the ones that are there, on the desktop.