I know I am very late to this party, but I think alpine Linux is the OS you are searching, I only used it in docker but it is indeed very small. (Only half a gig or something) also if something has a USB Port but not much disk space maybe use a live usb-stick distro like tails (also quite practical when you don’t want to be spied on). Hope that helps with a future project.

Because of the data efficiency thing. I think even when the saved CO2 is very minimal I think it is still better for people where the infrastructure is not as good or for people who can’t access the free net. The Tor network for example is run by volunteers and is not nearly so fast nor has the same capacity than the clear net. So keeping the traffic interactions but decreasing the data needed by the websites could benefit the Network.