Virtual thermostat and homekit

Hi,

I’m completely new to hass.io so please be indulgent.
Is it possible to have a virtual device that behaves the same way as Nest thermostat dose in HomeKit?
I’d like to be able to have a 4-state selector, ideally, on, normal, eco, and off, and a temp button that may allow to choose a different temperature.
The HomeKit icon will show the current temperature coming from a sensor and the target one (setpoint of a thermostat) like here:

The details view will look similar to what you can see here.

The off button should switch off the heater, the Auto may force the functioning for a certain duration, Normal will set the setpoint to 20°C, and Eco will set it to 15°C.

Thank you very much for your help.