Edit:
Try running Galaxy as Admin, worked for me.

Thanks for the suggestions. Actioning these hasn't helped, unfortunately, and I'm still waiting on a response to support tickets from six days ago. The web platform downloads don't start either, and there's no real indicator as to what I need to do. It's more than a little frustrating, and any other suggestions would be great.

Support tends to be quite slow. If you don't get a first response after Monday, I'd add a polite reply to the support ticket. "Bumping" the ticket this way one time usually results in a response.
If a few more days go by and you still haven't heard anything back, you can change your privacy settings to allow chat messages from everyone, then send a polite message with your support ticket number to a staff member like ponczo_ or Clownski_. I haven't heard from the latter after sending a message on January 5th, so it's not guaranteed to work, unfortunately.
Since you've already done the troubleshooting steps of disabling IPv6 and switching DNS to Cloudflare, and downloading via web browser doesn't work either, anything that filters or blocks connections would be the thing to check (firewall, router, HOSTS file, etc.).
If possible, it would be ideal to try downloading from a different device and/or using a different Internet connection. For example, if you can disconnect from your regular connection and use your phone as a mobile hotspot, support would be interested to know whether that works.

I am still having a problem with downloads. It just says server problem whenever I try to download through GOG Galaxy.

I'm having this problem too. Is there any solution?

also have the same problem was working perfectly fine last week.

I tried downloading a new game I just bought today. It's not letting me either. It says "Server Problem" when I try and install it.

same problem here, tried to update witcher 3 and cyber punk and nothing. unistalled them and tried to install and just gives "server problem"

Not downloading games database. Galaxy hasn't worked for me for months, tried the IPv6 option. Doesn't work. GOG needs to get its act together. All they offer me is to down load the games from their website which takes at least a day to do.

Any updates i Just switch a new computer and cannt download anything tried all the workaround

Same problem here. I'm so sick of Gog's BS. every month something new w/out any public notifications at all.

Same here. Fresh Windows Install and I cannot download enything from GOG Galaxy anymore.

According to down detector, all of GOG and not only GOG Galaxy can not download any update or install any game even as of now, at least in my area.

What error code are you guys getting with the downloads? I've had an issue with game updates on a mature install and it comes up with an E9 failure code. Looking that up, it seems like there's an issue with the servers