I recently had trouble on my Win 10 PC and I had to restore the OS from a save point. Funny thing happened: my BG2EE shortcut on my desktop disappeared. ( can't remember or reconstruct if the save point was from before or after my install of BG2EE. It isn't supposed to matter since I only restored the OS - depending on where the developers decided to hide all the application files.)

So I go to create a new shortcut, and I don't see any exes in the BG2EE folder. Now this seems weird to me, but I never looked there before. (Also, before you ask: I double-checked that my file manager options did not change so it hides exes.) Is this normal (if so, where do I find the exe?). Or is this as weird as I think it is (so I need to reinstall)?

I also have BG2 Complete edition installed on this machine.

I think that the system restore behaved the way it is supposed to.
It should monitor the whole Windows folder and some particular files' extensions outside there (mainly executables and libraries): this means that, according to the last restore point, there was no exe in the game folder, so the system restore deleted it.

As a standard rule, you surely have to reinstall everything that you installed after the restore point.