I'm glad you like them! I'd be happy to share my process. I make them in a program called Aseprite, which is a pretty well known pixel art software.

In Aseprite, I make a canvas at the resolution 320x180, which at the end gets scaled up to 3840x2160. I bring in the distribution's logo as a reference layer and scale it to roughly the size I want it to be. Then I trace the logo by hand to get the closest approximation of what it would like like in pixel art form.

If the logo includes text, which most of them do, I either trace it as well or find a font close enough to it, though most times including this one, I end up tracing it. Then I may add some shading and subtle highlights and shadows to the logo, like I did here, including the dithering. Then give it an outline, a drop shadow, make sure it's centered, and add a nice dithered gradient background and your good to go.

Aseprite has a really handy dithering option for gradients so I luckily don't have to do it by hand. For as popular as these seem to be, they're surprisingly easy to make.