I’ll echo the GPD sentiment already on display here. I have a GPD Win Max 2 and it’s not exactly pocket sized per se, but it is just about as small as you can make a traditionally laid out (more or less) laptop while still keeping it usable. It’s also tiny little gaming monster which is neat, but might be overkill for purposes. I carry it around in a pistol case rather than a laptop bag, just to be an asshole.

If you want to go smaller you can dry the GPD Micro PC which is roughly the volume of an OG Nintendo DS although its proportions are a little different.

If you want cheaper and don’t need the horsepower, one of my coworkers actually bought one of those little N100 based 8" micro laptop thingies, akin to this one, and I have some hands on experience with it. They’re sold under a myriad of non-brand names and I believe internally they’re all the same. It’s got about the footprint of a paperback novel although it’s much thinner, and could conceivably be put in a pocket if you wear Jncos, or possibly in a jacket. I was surprised at the build quality but the performance is rather dire, and using its little capacitive mouse nubbin for any length of time is an exercise in frustration.

All of these are truly x86 compatible, i.e. real computers, and come with Windows by default. They can certainly be bullied into running some flavor of Linux if that’s what you prefer.