Can a lift-and-slide door be as airtight as a normal door?

I hope it's due to the knowledge of the door mechanism

Rather due to the lack of knowledge of this mechanism :P I know some sliding elements from the 80s, they slide smoothly :)

(the brush seal is not the actual seal, but presumably mainly helps against dust and insects)

Not least, the brush seal is also about the (including acoustic) sand in the gearbox ;-)

There are no fundamental problems left to solve, so you can find good models.

You also have the free choice in this respect, as at least I am not aware of any manufacturers with significantly different design philosophies (or they make PSK instead of lift-and-slide).