Can't bevel round cutouts in a cube This seems to be a pretty typical problem. But reading many threads did not yet help me to find a solution.
I want to model a supposedly simple object. Unfortunately, the attached image is magnified. I have no idea how to make the image smaller. Looking at a smaller image makes it easier to understand the form.
I first tried to subdivide a base cube and model the cutouts, but this was not very successful.
The closest I came was using a boolean. However, I am not able to bevel the borders of the cutouts, regardless of the order of the booleans. When applying the boolean the geometry does not look too bad, but I still can't bevel the borders of the cutout, neither using a modifier nor directly.
I attach two .blend files: one with the boolean present, and one with the boolean applied. The design sketches can be found as empties in the .blend file.
Edit: @Chris. Your proposal did not help. This was my first idea as well. But if you look at the resulting topology after applying the boolean does not look too bad. I added another screenshot.


.blend files
I opened the first of the attached files, StopTablet2.blend... the Bevel Modifier was before the Boolean Modifier so I changed that. And voilà, the object was beveled. And even more after disabling Clamp Overlap.
In the second file StopTablet3.blend you've set Limit Method of the Bevel Modifier to Weight, but only the edges on the top have bevel weights assigned (you can see it by the blue color). If you give a bevel weight to the other edges you want to bevel it works, at least if you disable Clamp Overlap again. Or use a different Limit Method like you did in the other file.