How to handle heater with 4 settings?

I had the same problem but wanted to have the condition i could still use my manual thermostat on the wall in case of internet goes down. I used an ESP directly on my central heating unit that switches a on off relay on my terminals. Then i programmed the corresponding eco modes in HA. Maybe that can work for you too.

I don’t know how to get the data from your existing thermostat. I did not want to tinker with it myself