I am not sure if I have to do something special to make jupyterlab-git recognize the repository I'm in.
I have launched jupyter lab in the repo, and trying to use the extension I only get the following view:

I am running JupyterLab v0.33.4 with these two extensions:
@jupyterlab/git v0.1.3 (this extension)
@jupyterlab/toc v0.3.1 (table of contents)