There is git-notes for embedding information to git objects https://git-scm.com/docs/git-notes

There is also a project (probably many) for managing patches and/or issues in a git repository, but I can't find any links to it right now (can't access my github stars...)

Edit: there is also a alternative to git that has much of the same functionality of github embedded in the SCM itself, Fossil. https://www.fossil-scm.org

Edit2: GitHub back, think the project I was thinking about above was https://github.com/MichaelMure/git-bug which describes itself as "Distributed bug tracker embedded in git"