Just go with a Framework 13. Yes it's 13 inch instead of 12 inch. But you will get the best possible Linux laptop out there. And it's also fully repairable and upgradable. I have the latest Framework 13 AMD 7040, yes AMD. And... do not forget to select the new 2.8k display. Allowing for the first time to just select 200% DPI scaling that just works for Linux! So no scaling issues.! https://frame.work/nl/en/products/laptop-diy-13-gen-amd/configuration/new
Framework laptop 13 is just a bit above 1kg. It's 1.3kg... It is worth weighing this choice (you get the joke? hah, guhmm). If you really need something super compact and very light, maybe a old-school "netbook" will do.
Like the GPD WIN Mini (7 inch, that is super compact, right?).. But really get a Framework laptop hehe.