“homekit:HeatingCoolingMode” is just the item tag to tell Google the purpose of that item. On the Openhab side there can be multiple varieties (some of which you mentioned). However, on the Google side they all ultimately need to fit into: off, on, heat, cool, heatcool (e.g. auto) to work. Ideally, you’d want to have this item report/accept one of these values for the Thermostat to function correctly on Google Assistant.
For instance: Google will not know “Change Thermostat to Comfort” since it’s not programmed into the official Google Temperature Setting Trait
A workaround for now, may be to have an item Switch for “Comfort Mode” (example), then have a rule in OH2 that when you say “Hey Google Turn Comfort Mode ON/OFF” that rule will change the appropriate parameters within OH2 and the smart device. I do this for “Guest Mode” and “Work From Home” and it works. It’s not 100% ideal, but we have to work within the boundaries of what Google has designed and doing so will be time intensive.
Not perfect, but hope that helps!