Wow... and we use to think that a clean uninstall of Oblivion mods was a pain in the backside! Eventually a save game cleaner was made. But I do not see anything like that made theses days for today's games. I supposes it is becasue of how much more complicated the file branches and dependencies are now.
I think it's more that Beth games, and the Gamebryo/Creation engines were specifically built with mods in mind. It's how those engines work at their core. Hence modders got better and better at pushing what mods could do.
Not all engines are built that way, though. So now, mod authors have delved even into engines that are not inherently modular and managed to get mods working there, too. But it's definitely not "user-friendly / plug-n-play" to do so.
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On the OP's situation, here's how I avoid things like that with mods.
If I mod a game, I do the following (unless I'm already very familiar with the mods/games: )
1.) Back up all saved games, put them in a folder on a separate SSD/HDD, or save to an external device (flash drive, external HDD, etc.)
2.) Install mods, play around. See if I like them, etc.
3.) Keep eyes peeled for any sort of weirdness. If it happens, and I can't figure out for sure what's going on, DO NOT CONTINUE PLAYING. Immediately exit the game, delete any new saves back to the point I'm mostly sure things were working correctly and play through again. See what happens.
4.) If I detect a repeating or ongoing issue (meaning issues like progression, NPCs not working, broken mechanics, etc. -- anything that matters for gameplay,) I exit the game. Delete the entire saved-game folder. Remove absolutely all mods. COPY -- do not
move -- a backed-up saved game file into the save-game directory. Then, start the game and run it in vanilla, creating a new save in a new slot.
5.) I'm now back to 100% vanilla, and I can once again start adding mods to the game without worrying about whether or not there's corrupted reference data in my save.
^ Now, all o' that might sound like a huge pile of needless complexity, but it's not. It's absolutely required if I want to avoid future problems and ensure I don't lose too much progress if something goes wrong with mods. I always have 100% vanilla backups ready to go.
It's also a process that takes less than 5 minutes (in most cases) once you're used to doing it. Fast, easy, and vital to correct mod issues if they arise.
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The important thing to remember is to keep your backups "pure." The instant I save a game with even 1 mod running, the possibility of reference data becoming part of the save file is effectively absolute. At that point, my file is no longer vanilla and never will be again -- it's not possible to remove reference data from the file. It will be there forever.
It's actually
removing mods that causes many if not most of the severe problems people encounter. Having data references that no longer point to any data (because the mod itself if no longer there) can result in massive issues, up to and including CTDs when launching or playing the game. Once that happens, any level of fix will be hit or miss.