After a fresh install of hass.io, I installed the Git Pull add-on via the Web UI and configured it. I also installed the SSH add-on, and using that I made a copy of the initial config files from the fresh install of hass.io ("/config") to a new git repo. After I removed a couple of things from the configuration.yaml, the hass.io menu disappeared.
I cant figure out why this happens, since there is no specific config of hass.io in the default configuration.yaml.
Is there a way that I can get this back again?