HeresMyAccount: Well thanks, but one thing you all seem to be overlooking is this:
"...but I tried unplugging one, the other, and both, restarting the game each time, and that didn't fix it."
So if NO controllers were plugged in, then wouldn't it imply that they're probably not the problem? Maybe I shouldn't have mentioned them at all. It's just that I like to give a detailed explanation of what I've tried and the results that I got, in case they could be useful.
But really, if I don't have any controllers plugged in and it happens anyway, wouldn't that imply that the issue may be unrelated to that, somehow? Though I'm not sure what other issue it could be.
It might be also some other USB device, or even an integrated device, that is for some reason incorrectly recognized as an input device, either by Windows or the game. Or even just some driver.
In this discussion:
https://www.gog.com/forum/blood_omen_legacy_of_kain/veroks_gl_wrapper_patch/post20 for someone else it was the freaking USB webcam that was causing the issue. Not a gaming controller.
In my case that wasn't helpful because if it indeed was my webcam, I couldn't disconnect it as I was playing on a laptop that has an integrated webcam.
However, in my case, reinstalling Windows 10 fixed the issue for some reason (I reinstalled it in spring 2023 I think, so quite a long time after that discussion). Which leads me to believe it was some kind of USB driver issue, or some application or utility I had installed at some point somehow affected it. It needed a reinstallation anyway, it had had that same Windows installation since late 2018. Time to start from a clean table.
What is curious though that was the only game (GOG Blood Omen: Legacy of Kain + Verok's Patch, the vanilla GOG version did not have the issue!) where I had the issue, I played lots of other games on it without issues. And even that one problematic game got fixed by a Windows reinstallation.
I am not suggesting reinstallation will surely fix it also for you, but go figure.