Hello,
pressing TAB in the game doesn't open the console, although it's supposed to. In the user.ini file there is not bound a command to the TAB key. The corresponding line is:

TAB=

So, what's the command that toggles the console/chat window?
Thanks a lot!

Found it; it's Talk or TeamTalk.
But cheat commands entered there won't work, unfortunately.

That's odd, because Tab is working with GOG's version out of the box. Press Tab and the little input cursor appears. Enter a cheat command and press Enter and it gets executed.

Just to give finally the correct answer:

If you put some function on the TAB key and want to use the console:

open "User.ini" in the folder "Clive Barkers Undying\System\"

and put
"Tab=Type" (below "MiddleMouse")

OR

press "Defaults" in the control option menu to reset every key, then you can also use TAB again for the console, but you also have to reconfigure everything else

Some of the cheat commands turn themselves off when loading new areas. You need to bind a key to them instead of quickly typing them in repeatedly.