Cheers!

Is behind the throne included in the complete edition? I tried to buy but I got the message saying it is already included in the complete edition which I own, but it does not appear in my bib.

Same problem here:
"Please note that Old World - Behind the Throne is already included in Old World: Complete which you own."
But this new DLC ist not listet inside the description of the Complete Edition:
https://www.gog.com/de/game/old_world_complete

Soeben gekauft! =))))))))))))))))

Herzlichen Dank! =))))))))))))

On Steam the Complete Edition is updated already, but not on GOG.

How I dislike this neglect of GOG by the publishers... The release date is often not relevant at all for GOG users, as there are always so many problems and delays here.

The Complete Edition is just a collection, as far as I know you only get the contents it had when you bought it, so it should be correct that you don't own the new DLC, if you bought the Complete bundle before yesterday.
The warning is not technically incorrect since right now, it does contain the DLC, but it's misleading at least, and should be ignored since it doesn't matter what it contains now, only what it contained in the past at the point when you bought it.
If you can't buy the DLC because of the warning, you should write a ticket to GOG support.Complete Edition already contains the new DLC on GOG too - you can check on gogdb: https://www.gogdb.org/product/1302016290#references -, it's just the description that's outdated.

Why has the description not been updated to date?

I have asked the Support. All future DLC for a Complete Edition will be automatically added to owners. Behind the Throne should automatically appear in your library. This sometimes doesn't work correctly. Support will send you links with which you can refresh your account and library. Then the DLC will appear in your library.