Is there any reason it is not possile to modify the Hestia-Pi .img to:
accomodate the relay board
add additional temperature sensors
modify thermostat logic to perform feedback control for 3 ACs?
Sensors and actuators (relays) will be controllable / readable from Python. If Hestia-Pi is a sensible starting point for my project, then it is very attractive because it is designed as a HVAC controller (thermostat)
The software is openHAB but you are asking about more than than just the software. Almost no one on this forum will be able to answer your questions. You need to ask on the HestiaPi forum.
What I can say, given my experience with it thus far, is that it would probably be less work over all to start from scratch. But it might be useful to get it and play with it to see an example.