HA thermostat (not phisical) that can do cooling and heating

Hi all,
right now I’m using the climate entity to set the house temperature, but it doesn’t send out any MQTT message, so I can use it only for the temperature and ON/OFF, but can’t use it to control the heat pump (underfloor heating).
With the generic thermostat it should be possible (I’ve been told but I haven’t investigate it yet), but it doesn’t support both heating and cooling.
So, how do you guys manage heating and cooling in HA?

It seems nice and well maintained, I’ll give it a go!
Thanks!