I noticed that polygon-polygon collisions have a similar issues to the one circles have.
Center point outside of lager polygon:

Center point inside of larger polygon:

I want to properly solve all the issues before this can be merged.

I've fixed the polygon-polygon mtv calculation.
Your implementation of the overlap function was faulty.
Checking for the min/max of both may be quicker but it does not handle intersections in which the min and max of one projection are contained by the other projection.
In the example I gave in my last comment the mtv becomes the width of the smaller polygon.

Regarding the polygon-circle mtv calculation.
The approach to only check against the polygons vertices and the center of the intersecting points is clever but can lead to wrong results.
I propose two different solutions:

1. Only add the intersection center point to the checked vertices if it is not contained by the polygon.
   This means that there are some cases in which the mtv is not actually the minimum, but only in cases in which the current solution would give incorrect results anyways.

2. Solve it the traditional way, that is:
   Project the circle against all polygon edges and find the minimum overlap.
   Keep the check against the polygons vertices (without the intersection center point)

For now I've implemented solution 2 as it does not have any corner cases.
Hope I didn't make any mistakes.

This should be ready for review now.

Finally, haha! Excellent - thank you very much for the contribution! Really appreciate it!