Please note that this is the German Q&A Forum, any content should be posted in German. However, based on your post, I will assist you in English today.
Hello Streifenkarl,
This is often caused by another app or overlay taking display priority. Please fully close overlays or recording tools such as Xbox Game Bar, Discord, Steam Overlay, or the NVIDIA/AMD app, then restart the game and check Exclusive Fullscreen again.
If the option is still unavailable, particularly if this started after a game update, I recommend contacting Activision Support because the display-mode option is controlled by the game.