I think you will find the CX bike more than capable on pavement.
I’ve used my Focus Mares CX bike for everything the last few years. CX races, gravel, dirt trails, crits, fast group rides. It’s been absolutely fine.
Recently I came into a Trek Emonda. I just recently finished getting it built up. I have a forest preserve road here, that is actually used for practice crits in the spring. I use it for TR workouts outdoors. I was curious about the speed difference, so I compared average speeds during sweet spot intervals. At the same power, the Emonda was 0.5mph faster at 260 watts. I should also add the Emonda had aero shaped drop bars, and was on tubeless GP5000s, whearas the CX bike had tubes (latex). So I would say the difference between the bikes was just a couple tenths of a mph, if that. I wouldnnot be shocked if rolling resistance and bar shape comprised nearly the entire difference of 0.5 mph.