These are amazing illustrations, but I don't understand the emphasis on pressure differentials. That is not how wings generate lift. Due to attachment they deflect the flow, and the momentum change generates an upward force [1]. The practical point of understanding the flow over the wing is to keep that flow attached so that you can deflect it or reattach it if you get out of sorts.
1. https://www.grc.nasa.gov/WWW/k-12/VirtualAero/BottleRocket/a...
He should have started his lecture with the chart shown at the 26 minute mark. Saying when we measure the pressures on the airfoil, we see high pressure at the front and bottom of the airfoil. Let me explain what is going on…
I found his explanation at the 13 minute mark to be hand wavy. He talked about flow turning and momentum change but just hand waved away why pressure is higher at the bottom of the wing.
You are correct in that the deflected airflow exerts an upward force on the wing (or at least a force with an upward component; there's also a backward component (called induced drag if my memory serves me well)).
The way the airflow exerts that force is through pressure differentials: air under the wing having higher pressure than the air above it.
Momentum change can describe physical interactions, and it's often easier to calculate things that way, but actual physical forces still exist, and can also be used to describe the same physical interactions.
The explanation you described is the greatly simplified "high school friendly" explanation. It's not wrong, per se, but it's incomplete.
Even your link explains: "The net fluid force is generated by the pressure acting over the entire surface of a closed body. The pressure varies around a body in a moving fluid because it is related to the fluid momentum (mass times velocity). The velocity varies around the body because of the flow deflection described above."
I.e. pressure differential is experienced as lift and is caused by the flow turning.
Explaining the actual cause of the flow turning and resulting lift (and why attachment is maintained along top surface) requires looking at fluid dynamics/navier-stokes including pressure differentials, viscosity etc. The pressure differentials allow a more comprehensive way of breaking down the forces at play.
I like this video for a more comprehensive understanding without getting too in the weeds with the math: https://www.youtube.com/watch?v=aa2kBZAoXg0