I get redirected to:
https://checkoutshopper-live.adyen.com/checkoutshopper/threeDS2.shtml?pspReference=<snipped>
and there I only get a twisting circle. See screenshot 1.
I switch to Microsoft Edge, the checkout basket still has the item I put in when I used firefox, I check out, and it works just as usual.
Why are so many sites starting to fail with firefox, and GOG is now among them too? Google dominating the browser engine market is a real issue.

Are you using any scripts or plugins that might cause the problem? I just tried with Firefox and had no problem with the checkout.

You broke the site with your add-ons. uBlock Origin, NoScript, and any other content blockers would be the prime suspects.

That is a snap judgement - If you look closer: They are both inactive on GOG, nothing is blocked, and nothing is blocked for that weird "adyen.com" site too.
It worked until my last order before, which was 6th of June. And all orders before over more than a decade.
There was a firefox update in between. But this does not change the problem: Edge and Chrome are updated more often, and GOG fixes the possible problems before they arise since they check with the preview builds. But for Firefox: Nobody cares and more, including GOG.
GOG is not the only site, more and more sites start to fail. We are doomed to rely only on one browser engine ind the background (well, Webkit too if you count in Safari...).

Works fine here on latest 114.0.1 (with strict protection settings + uBlock Origin).

Well, I will see with the next order. Maybe it was a temporary website problem, and I just had bad timing...

EDIT: Worked fine today (four days later), browser still same browser version and same ublock/noscript config (blocking fecebook, quite a few google sites and salesmanago).

Baught sth. yesterday without problems. Now that I've seen your post, I've uptated firefox to the latest version and had the same problem (checkout error after adyen page load).
But after disabling umatrix it worked fine. So it's either a new script requirement and/or a firefox quirk or whatever.

edit: could be that for the paypal domain script and cookie must be whitelisted now (even when not using paypal).

Checkout works fine with the latest version of Pale Moon (32.2.0), even with uBlock Origin installed and enabled. And has done every time I've made a purchase while using it. :)

Just note that sometimes uBlock is known to still function to some level even if you turn it off for a particular site. You actually have to go in and disable the extension itself in Firefox's settings if you truly want to test if it's that extension giving you problems.

But yes, I have noticed that over time more and more websites don't work properly with Firefox any more. Not that those websites ever stated directly that Firefox was a supported browser though.