The bluescreen message is SYSTEM THREAD EXCEPTION NOT HANDLED and it claims bcmwl63a.sys is what is failing.

I have tried a lot of things to fix this issue, but so far nothing has worked.

It is also notable that it is only when trying to download a game from gog galaxy that this happens. I have not yet tried to do it from the browser, but I want to use gog galaxy in the future. I am currently trying to download a game from steam to see if the issue also happens there, but it seems not so.
It also doesn't happen anytime else.

It would be helpful if you could tell us what you have already tried so that we don't suggest things that you have already ruled out.

Did some quick research and repeatedly found that it might have to do with wireless devices and their respective drivers. Might that apply to your setup? https://www.minitool.com/news/bcmwl63a-sys.html

I obviously too found that site and tried everything there and nothing worked.

running systemfilechecker did claim it found and fixed something, but the issue persisted

I ended up resetting the pc, choosing the option to keep my files. There has been no bluescreening yet, but there are a couple of things that worry me slightly:

Almost every gog installation at some points say installation failed. Clicking retry does eventually finish the installation and I can play them, but I never had this problem before

When surfing the web and clicking on links, I get for a few seconds and error screen that say it can't connect, before automatic reload and connecting. Another small issue I can live with, but would prefer not to, that I've never seen before and I'm worried about what bodes for the future