Just to clarify, when I say that I exited the browser, I mean that I did so by going to the menu top right and clicking exit. That way all running extensions also get terminated. But either way, as far as I can see I don't have any media related extensions installed.
I already have VLC set as the default music and video player in Windows settings. Still I tried changing them to a different program, relaunched explorer, and the keys still didn't work.
Plugging the keyboard into a different port (front i/o instead of motherboard) didn't change anything either. But I really don't think it's hardware related, because as I said, the keyboard tester is registering the media keys. They're just not functioning in Windows. I even tried the keyboard on my Win10 laptop, and the keys work fine there.
I also tried turning off 'Show desktop overlay when using media keys' like you said, but that didn't change anything either.
I'm really stumped :/