Not at all.

Imagine two roads, parallel mostly, but then one takes a detour, like this:

         ____
    ____/ __ \____
 -> _____/  \______
    _______________
 -> _______________

Now imagine them full of cars, bumper to bumper.

Now imagine the cars move, at the same speed, on both roads. Same number of cars will come in on the left as go out on the right.

The cars will be bumper to bumper, both on top and below (there'll just be more cars on top).

Why should cars that come in at the same time on the left exit at the same time on the right?

The air was already there, the wing is being pushed into it, it seems to me that when the wing has passed it needs to end up all touching the same pieces it was before otherwise the wing will leave gaps in the air.

But the air does move faster above the wing without joining back up with the air moving below the wing, see the video jgord shared https://www.cam.ac.uk/research/news/how-wings-really-work

air being incompressible makes even less sense, given how daily the experience of compressing air is