I had no issues at all running alpine with a UI on a simulated 128MB RAM machine with a few GB of storage (with simulated 2000's disk speeds). That's 128MB not counting memory for the BIOS, of course.

i3 and NetSurf made that extremely possible. Mind you, the only things that didn't work well were Firefox (wouldn't launch due to OOM) and compiling Rust projects. Single translation units in Rust would immediately OOM the system, whereas C, C++, etc. worked fine.