Nate (The Creator of NLP) has addressed this in this thread: Idea: Expanding Negative Lab Pro compatibility to other software platforms like Capture One, Affinity, Luminar, and Lightroom 5.
In short, the limitation lies in Capture One’s software development Kit lacking the necessary features for NLP to be transferred or even created to work in CO (or other apps).
Hope this helps!
Wishing you a day as captivating as a perfectly exposed analog photo!