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As of R2023b, you can use export function of MATLAB to export markdown from livescript.
Here's a small document (in Japanese) on how to use export to convert livescripts to markdown.
When exporting to LaTeX right after running the livescript, it's observed that the figures will be exported as eps files or not at all if the livescript contains more than 20 figures.
I suggest that you close the script and reopen and then export to latex.
This repository provides a functions to convert your live scripts to markdown file. I hope this function makes your life easy to document your repository.
I've checked the function with multiple live scripts but please note that it's not perfect. It's expected that you need some manual editing.
Hope it accelerates your MATLAB life. Any comment and suggestions are always appreciated.