Check your spam folder.

Not there.

Is it being sent to your current email address?

What email provider are you using, within a reasonable factor?

Yes, the 2-step authentification is broken. Sometimes it reacts to logging in from the same computer. Or even when I am already logged in, but want to change my profile picture, for example. But sometimes it doesn't trigger at all even if I log in from a different computer in a different country. It seems to be completely random, when and how often it triggers.

Yep current address is correct at gmail.

I suggest you contact Support as it's quite unlikely any GOG staffer is going to catch this thread, especially with the sale. And even the CM, Linko90, who monitors the forum, will tell you to contact Support. This has happened to me quite recently, and not only was it the same device, it also was the same IP address. It's definitely a lot less reliable than the description makes it to be.

for me on windows 10 with firefox it usually works as intended (no reaction to same computer and such). Also never having issues getting the emails but using a smaller local provider so cant offer insights on gmail and such