Non linear vector distortion

Hello,

I need to obtain a circular file from the rectangular file.
As you can see, the difference in latitudes is not linear, there is a narrowing of distances.
On the other hand, longitudes are regular.
I therefore thought it would be useful to perform an initial deformation on the Y axis, followed by a circular deformation. This seems simpler than a one-step deformation.
You have to understand that the grid is there for calculation purposes, but in reality there will be vectorized text and logos...
Thank you for your advice or help, it's a great help.