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?

If you've already done these steps, then open a support ticket.

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