Edit: “Updating to the legacy 580xx drivers doesn’t show me a desktop anymore”, just in case someone else can stumble upon this by searching something similar.
Thanks to @deadcade@lemmy.deadca.de and @Ooops@feddit.org I did try fixing it out of curiosity. I had forgotten to install linux-headers. Hopefully someone who actually has the same problem as me, and needs to fix it, can use the tips given in the comments. On my end, I just had to install linux-headers and one reboot later it worked.
Always check if you have all needed packages and don’t just “remember” that you had them installed.
Boot into a live boot install of some distro on a USB drive.
I did try that as well. The legacy drivers did install from the tty, still the system doesn’t see them, for lack of a better word. It is not a big issue though. I had already planned on upgrading since my current setup is very old.
Half of the new components have already arrived. The current PC will become a little home server running either Ubuntu or Debian most likely.
I just thought the situation was funny.