In this blogpost I describe what I did to get AsciiDoc support into Gitea. If you want more than syntax highlighting and basic formatting, Gitea has to be patched unfortunately(this issue has already been reported). But I think most people will only need to edit 1 configuration file and are done.
Asciidoctor or AsciiDoc? Asciidoctor has inbuilt support for highlight.js, the solution Gitea uses and is therefore the best choice in most scenarios.