I used a cd key for an older game version, and of course found out that I cannot play online using that key with the EE version of the game.

In the old version, you could edit the nwnkey.ini file and update your cd key. Unfortunately, I am unable to locate anything similar in the GOG installed EE version.

How can I correct the association to the new GOG provided cd key that I obtained from logging in via browser and checking my licenses?

A file named cdkey.ini, located in the directory %USERPROFILE%\Documents\Neverwinter Nights\ should contain the serial key of the game.