I find it utterly implausible that these filters have any substantial effect on NOx. There are specialized filters consisting of large beds of modified carbon that will remove NO2. Regular activated carbon AFAICT does not, and these recirculating stove filters do not have massive filters.

I would believe they remove particulates and odors, and that’s about it.

While they have filters (which I've never known people to replace, but that's not necessarily the hood's fault) and I believe they do something with what passes through them... they unambiguously miss the vast majority of the fumes. Even if you cook with the back burners, a massive amount of heat and steam will flow right around every hood I've run across.