Can you also hear how it seems not only to be a volume thing but also affects the perceived "openness" and kind of "steps back", "compresses" for the lack of better words? My guess (without in-depth analysis) is that the transients with their high frequency content get compressed which results in a slightly muffled, less open sound.
I have not had enough experience with the new Kemper Drive to know how it interacts.
But what you describe above seems normal to me.
With most tube amps (at least Fender amps - that is what I’m familiar with) you can raise the volume knob a certain amount and get more volume, then you reach a spot where you get distortion AND more volume, but then there will be a point where you don’t get any more volume but rather more distortion and compression. That seems to be what you’re describing.