Ok, I tested a few additional mesh settings and calculation settings. In this post, I will also make a quick summary to defend my proposition of the of solution.
To properly solve the compressor simulation we need to have the possibility to catch the thermal gas expansion to determine the density difference between the inlet and outlet. Autodesk CFD is able to catch it only in subsonic simulation.
From the second side, we need to use a rotating region with a small degree time step to catch changing position of a blade and frequency of the compression(that pressure plot a few posts above). The field at the end of the simulation should have a repeatable value and should depend on the position of the blade.
When I try to solve the simulation with moving blades and subsonic flow, every time I get extremely high velocity neat the wall layer which later in a few iterations filled the entire domain and software crashes. Reducing the wall layer size, increasing the amount of it, decreasing the time step, and changing boundary conditions do not solve the issue.
With that, we could try to solve the simulation in the approach which I proposed at the beginning with a steps solution with a quasi-steady-state at the beginning and later decreasing the time step and compressible flow, but that will not change the density of the fluid properly or just compute the quasi-steady state solution with the subsonic flow.
I personally think that the second option is better. Even if we do not have to catch the change in time, we cover the physics behind the process correctly.
So long story short, stop the simulation on the first step( number of blades 1) and run the simulation for 600 iterations.
The results should look like that.

Probably we will be not able to get something better.
BR
Karol