So, can't sign in or create a new account on the GOG version. It just tells me the connection was interrupted or something along those lines.

Then I happened to come across my old CD copy of WarCraft II BNE. Just for the fun of it, I decided to try out and see what happens if I try to connect to Battle.net.

As strange as it is, it works!

Gives me multiple alternatives instead of "Global". I was able to connect to the European server and even register an account. Even the email verification works

Global was offline for about an hour today but it now should work properly.
If you are looking for players to play with we play every weekend with friends and are very welcoming :-)

If you remove Win Registry entries about game from HKCU game recreate it with older servers gateways. But it not possible to connect to them from GOG version. Im too lazy to check my CD version (and 2.02 separate patch). Im sure it not work on Bnet Global ("gog" server that is not from gog ofcourse).

If Op is right, both versions are separate. And that mean same for Diablo 1.
Blizzard mess with them all availability few times. Sometimes for long period (before fixing back). So on any on them there is almost no one who play. Since 2020 (? i guess) when first time Blizzard mess with servers availability...
people play on war2ru mostly. It possible to add this gateway as alternative. It possbile to add older 4 servers and keep Global in list.
But with that 6 servers it possbile to connect only to Global and war2ru.

There is still someone who play on Global. Also, GameRanger support Warcraft 2, but looks like only non-Bnet version on Apple Mac.
But that only for few ppl. About 20-30 on war2ru. Sometimes few dozens more
http://server.war2.ru/status