Every single game that failed to download had an empty folder inside OBB, which was inside another folder named com.vending. I don't remember this folder from the past, but that doesn't seem like a coincidence.
This old thread eludes to this possibly being my exact problem.
Hey, I got a problem. When I try to download/upgrade a game or an app with obb files, Play Store starts the download but It stops when it's almost finished and says error code: 0 I tried to reinstall Play Store, delete the cache, and other...
forum.xda-developers.com
Edit: No dice, they solved the problem via activating all permissions, but this didn't help me.
Edit 2: In the end I was able to fix it by going into Permission Manager X and changing WRITE_SETTINGS from default to allow, and USE_ICC_AUTH_WITH_DEVICE_IDENTIFIER to allow.