I have an Orange PI Pro 5 16GB on a box that smoothly runs a full blown Ubuntu Desktop version and would fit in a pocket though it’s maybe a little too thick (from memory the box it’s about 3x5x2 cm).

Total cost was about $170.

The board itself would fit a thinner box, but you might have to 3D print one.

Mind you, a N100 Mini-PC that costs the same is even more capable as a Linux Desktop, but it’s significantly larger and will definitely not fit a pocket.

You can find cheaper SBCs capable of running a Desktop Ubuntu but in my experience (with a $35 Banana Pi P2-Zero) if you go too far down the price scale Desktop Linux performance stops being smooth, even if the board is a tiny thing.

It was actually quite surprising for me recently when I found out some of these things are perfectly capable Linux Desktops.