sub-sonic, trans-sonic, and supersonic aerodynamics are fundamentally different. You’re calling out some differences, but not covering others.
They are wildly, fundamentally different in behavior.
You’ll notice that supersonic aircraft have different airfoil shapes, different airframe shapes, and wildly different engine configurations because they don’t work the same way.
There is of course air behind the Mach cone, but it is much lower pressure, will often completely separate (airflow wise) from the airfoil shape in ways you would not expect, and the shockwaves/speed of propagation can cause bizarre pressure, lift, and drag issues. You can end up with massive vacuum where you previously had pressure, or pressure where you preciously had vacuum. Transonic flight or high angle of attack flight at supersonic speeds of course produces rapidly changing variations of all these effects.
[https://arc.aiaa.org/doi/abs/10.2514/8.1394?journalCode=jans]
Unlike subsonic flight, the air can’t “get out of the way” in time, leading to potentially catastrophic issues without careful design. Supersonic flight is better categorized as ‘shoving through slow air’ than flight.
What you’re referring to is not wrong - just doesn’t reflect the magnitude of the actual differences