Given the lack of recent (using the term generously) activity for ob-julia, I think it is safe to assume that it is abandonned (unless there is something to suggest otherwise). I don’t see a license in the repo, so I guess if someone wants to use it, they should start a new project for the same purpose.
FWIW, I switched from org-mode to Markdown for the same purpose. org-mode is of course much more “powerful” because you can customize it directly with Emacs Lisp, but because of this, 3rd party tools have a difficult time converting your document, also, 3-5 years is enough for that Emacs Lisp code to go stale. Markdown seems much more timeproof because it is just a markup syntax, not a markup syntax plus an insanely powerful and versatile programming language, hundreds of packages, and the decades of cruft I copy-pasted into my init.el.