Simply changing a registry entry isn't going to get VS working again. VS used to store everything in the registry but since at least VS 2017 they moved to storing a lot in files on the file system to help support multiple instances and removing the clutter in the registry.
At a minimum, besides all the registry entries (there would be shared entries + the instance specific ones and they are both in HKLM and HKCU. You would also need to find and update all the file system files that are impacted. For example all the package management tools store stuff in your AppData directories.
I'm not sure how you "reinstalled" VS but I don't see any way of recovering short of actually putting a new D: drive on and then running the VS repair. If you don't want a new D: then after you've repaired the installation then uninstall all of VS and reinstall to the C: drive.
The specific error you're getting looks like a Nuget caching issue to me. Nuget isn't finding a package when it restores and it is walking through the file system locations that it would normally store packages to see if it can find it before it tries to download again.