Can a note be pushed to origin?

In a project that I am working on, some metadata is currently embedded in some source files. The question was asked yesterday if there is a way to move that metadata a git specific file and link it to the source file or commit.

I remembered that git has notes which can be used to add such data to a commit, but I don't believe that such metadata gets pushed to origin nor fetched from origin but another user.

Is there a currently implemented way to do something like this?