Not many wiki site engines based on Markdown work directly from git as cleanly as this.
There's a few of them though, such as this old Ruby lang standby with a decade's worth of features that a decade ago was a way to host your same GitHub Pages site locally, supporting SSO:
https://github.com/gollum/gollum
https://github.com/gollum/gollum/wiki/Gollum-via-Rack-and-CA...