Long ago the UI was actually hosted on Homey itself and the device was really usable offline, but at some point (firmware v2.0 I think) a lot of stuff was moved to the cloud, including authentication and discovery. In theory, Homey (Pro) can run offline for a short while (until the authentication token expires), but in practice it depends on Athom cloud services (even though Homey is marketed with “Everything Local” 
). And that’s only if you were already authenticated; if not, Homey will just not be usable offline.
I doubt the my.homey.app UI will ever be shipped as part of the firmware, for the simple reason that it’s an eternal WIP and shipping an embedded version means for every change a new firmware needs to be published.
IMO Homey is a cloud-dependent home automation platform, and I don’t want such a dependency, so it’s one of the reasons I moved to Home Assistant some time ago.
