I used Home Assistant before Hubitat, though with the states UI and not Lovelace at the time, and honestly find a dashboard--in any conventional form--much better for manual interaction via phone or tablet than a UI like the above, which appears to more or less be standard Lovelace with a couple added cards. It can be customized quite a bit, but while neat and apparently optimized for the device it's being casted to, this honestly doesn't look like much more than what you can already do today with a copy of Home Assistant running on the hardware of your choice. That is more or less what I'm still doing now (but with Lovelace), integrating a few devices I care to have in Home Assistant via MQTT.
The floorplan you see in the screenshot is not part of the Cast integration specifically. It's actually not part of Home Assistant at all--it's a third-party integration, but one you can already use today as a custom Lovelace card.
Nothing is stopping anyone from creating a similar third-party integration for Hubitat. (Or just taking what I'm already doing above and just taking it one step farther--I don't think I have any interest myself.)