I guess some renderers have some option to calculate extra supbpixels in needed areas in order to avoid post anti aliasing? Am I dreaming?
You’re not, but Cycles already has that feature. It can’t work with a sharp pixel filter though.
What you want to do isn’t really achievable in the render. Cycles is already really, really sharp due to not just being a render, but the somewhat odd pixel filtering method it uses which prevents neighboring pixels from influencing each other. In other words, Cycles renders are naturally about as sharp as is mathematically possible with rendering techniques. It’s also far sharper than any physical camera could achieve as it is not limited by silly things like diffraction and debayering.
If that’s not enough local contrast, a 2D sharpen filter like the ones in your example is a good way to go. These filters don’t actually make the image sharper, kinda the opposite as they draw strokes around the edges of things. But the improve the contrast of edges, making the image appear sharper even though it isn’t. Your can see this in the rug in your example images. The sharpened version makes the fibers easier to see at a glance because their edges are higher contrast, but if you zoom in there’s actually less detail because that contrast boost (the unsharp mask) covered up some detail.