MasteR
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I forgot about the NFH mod. I have it installed, but even with the mod that adds a skill wheel to the game itself (although the first time, there was no skill wheel, and I still couldn't enter without casting a spell), I couldn't get in.
I have a save file, and I even started replaying this mission for the second time, hoping that this would fix the bug, but it didn't.
It seems that NHF is affecting it; I haven't encountered this bug during numerous tests. I could fix this using the console in the save file, so you can continue playing.