I've checked the "More > Serial Keys" path. But under the "Serial Keys" there is only a key for the BG2 Enhanced Edition. Nothing else. I've got the game on sale. Is this a problem?

I'm pretty sure on GOG that if you buy the Enhanced Edition, you get the classic version for free. (That said, EE apparently runs better on some modern systems.)

Ok, I figured it out.
The serial key for the BG2 Enhanced Edition under the path "More > Serial Keys" is the code that must be used to redeem the complete edition. It was little confusing - using a enhanced edition key code to obtain the complete edition.
Anyway, Sorry to bother you with my post.
One more thing - the BG2 Enhanced Edition serial key had an expiration date. Mine was year 2033.
So don't forget to redeem your complete editions.

Yes you get the classic version with the EEs, but you have to specifically ask for it.

And yes it expires, too, which I dont like either, but then again I've already downloaded it, so for me personally its not a problem.

Also GoG may decide to prolong it after all.