I usually put a badge like this in README with
[![GitHub commits since tagged version](https://img.shields.io/github/commits-since/USER/PACKAGE.jl/vX.Y.Z.svg?style=social&logo=github)](https://github.com/USER/PACKAGE.jl)
and then use it as the docstring of the module by this one-linear
@doc read(joinpath(dirname(@__DIR__), "README.md"), String) PACKAGE
so that the badge is included in the documentation (e.g., https://tkf.github.io/BangBang.jl/dev/#BangBang.BangBang). I like that it provides useful bits of information while also providing the link to the repository (though it relies on that people already know that badges are often clickable).
For fun, you can find other github-related badges in https://shields.io/ (type github
in the search form).