When you're adding the game manually it asks for the "folder" that the EXE is in. Since it's only looking for the folder it won't show the EXE file (or any files). You just need to select the correct folder and you're good.
Y'know, this was information for how it affects real users. It wasn't really a request for suggestions on how they should do their job. This is just the part of the protections that's visible to and could affect some mod authors not all of it.
It pretty much already exists. Go to the main page for the game you are searching for (for Fallout 4 it would be: https://www.nexusmods.com/fallout4 ) then click on the "mods" drop down menu at the top and select your download history. It will be filtered down to just mods you downloaded for that particular game.