A two-fold question:
First of all, why is my bevel modifier not doing anything? Does not matter what values I put in.
And if I would add a bevel with Ctrl + B, the back edge of the shape is doing something different than the front edge as you can see in the picture below.
I just want to use a Bevel Modifier so I can change it later if necessary.
Secondly, would it also be possible to use a different bevel amount on the edge of the circle than the edge of the outside shape?