As you said it won’t tell you if the air is being filtered. I think you’re better off measuring the small particle content of air if your concern is viruses, or both.
PM2.5 sensors or other things like what you're thinking of do have their place, but they also have a bunch of other issues - they'll be detecting VOCs, brake and tire dust that's fine enough, any aerosol whether it's coming out of a mammal or not. I think it's inaccurate to say they're just a generically better solution than CO2 monitors for viral risk.
But yeah, as you said, the best aspect of a CO2 monitor is that it gives you a useful upper bound for the general respiratory virus risk in a space.