I recently got CoP on Steam and I discovered that you can reclaim it on GOG, but for some reason it isn't working, does it not work if it's the key given by Steam?

If you're talking about the reclaim program, it should only work with keys from boxed copies:

https://www.gog.com/reclaim

However, this thread claims that steam keys for the stalker games should work as well (or they did in 2015 at least).

So if you can't make it work, the thing the poster in the above thread is talking about might be an unintended mistake that has been fixed since ¯\_(ツ)_/¯

Well, I've tried it various times, I've copied it from regedit, from steam, typed it out myself, just haven't seen it in game but I don't think it would change much.