Just be aware that the Elite remote control's 'home control' buttons are really designed to be used with an official Harmony Hub integration, with other systems such as Philips Hue, Lutron Caseta, and SmartThings. Using these official integrations, one can map the 'home control' buttons on an Elite remote control to various switches and dimmers that are exposed via those official integrations.
Since Logitech is not accepting new official integrations, Hubitat has not way to create one. Thus, I wrote an unofficial community integration for Harmony Hub. The Logitech application and cloud servers have no knowledge of the Hubitat hub. I am using a local webSockets connection directly to the Harmony Hub to request a list of Harmony 'Activities' that are then turned into child Switch devices that Hubitat can use to control and monitor the current active activity. These switch devices can easily be used as triggers for whatever Hubitat automation you desire.
Recently, I worked with another community member to add some very limited support for the Elite remote's 'home control' buttons. In order to use them, one has to map these buttons to devices expose via one of the official integrations. Using SmartThings is the simplest way of doing this, as one can create a ST account for free, without a hub. Afterwards, simply create 4 virtual switch/dimmer ST devices, and then use the official ST-Harmony Hub integration to map these virtual buttons to the remote's 'home control' buttons. Afterwards, it is possible for my Hubitat Harmony Hub integration to 'sniff' the webSockets traffic to identify unique IDs for each of the buttons. Once the user completes that portion of the process, the four home control buttons will generate 'Button' pushed and held events in Hubitat, that can be used in whatever automations your desire.
(Note: there are more details available in my Harmony Hub Integration thread)
