Is it possible at all? Where can I find the codes required to do it?

I would also like to know that for EU:Rome and For the Glory. The method should be the same :)

Came here for the same reason. My ticket (issuer) with Paradox didn't seem to know where on GOG.com to look for these unique codes. I was asked if GOG was refusing to give them to me. I said "No, I just don't know where to find these codes."

Adding Paradox "Owned" Games to Paradox Account:

https://support.paradoxplaza.com/hc/en-us/articles/115001367547-What-is-Owned-Items-and-how-does-it-work-
IMPORTANT NOTE ABOUT NON-STEAM GAMES!
If you buy a non-Steam game (GoG, physical disc etc) you will be provided with a code (usually starting with four letters followed by numbers).

You hover the mousepointer over your username in the menu at the top of the screen so that a contextmenu appears.
There should be something like "Games (300)" (in german it’s Spiele and the number of games you own on GOG). Click that to go to your game library. Click on the game in question or use the search function to find it (e.g. for me the Europa Universalis game For the Glory). Click the picture of that game to see all the content of that game that you own.

In the top row of that game there should be your system (e.g. Windows), language (e.g. english) and "more".
Click "more" and in the appearing menu for me the 2nd from the top was "CD-Keys" and once clicked the key for the game.

If you haven’t done already create an account on the Paradox forum
https://forum.paradoxplaza.com/forum/index.php?forums/

and then click the button at the top "Register a Game" which will bring you to
https://accounts.paradoxplaza.com/redeem
where you can enter / copy&paste the key of the game you want to register.

I pasted my CD-Key for EU 3 from GOG, which resulted in an error message: „The code you entered is invalid“. Anybody else with this prob. Any ideas?

For EU 2 there even isn‘t a CD-Key...

Send a support request to GOG, they have to get a key genereated for Forum activation. This is due to the GOG policy around these old games that use CD keys IIRC. They use a Master CD key for the game in install. For multiplayer and forums you need a unique key.

This is the list of all available badges you can gain on the Paradox forum, e.g. for registering a game
https://forum.paradoxplaza.com/forum/threads/paradox-interactive-forums-o-medals-icons.1188414/

There is one for "For the Glory" or for EU III or EU Rome.

But for the oldest titles like the original EU and EU2 there is no forum badge to gain from registering.