It is important if you are putting in a new HVAC system that you understand what Hubitat can integrate with. The variable speed systems that require a custom thermostat do not integrate in to Hubitat. They almost all closed systems.
I have owned and recommend many of these in the past but I have since changed my opinion after living with them. These systems can not be easily fixed and parts are NOT readily available and they break down far more. I have spent so much more down time with the variable speed systems than I ever did with a single speed system. Also with single speed systems I can install my own thermostat that cleanly integrates in to Hubitat.
Single speed systems can be repaired by any parts. Most repair guys have the parts in their truck!
My recommendation is a US Made 16 seer single speed system with an Ecobee, Z-wave or Zigbee thermostat; integrated in to Hubitat.
I have a multistage/multispeed Goodman that works with any thermostat (I'm not sure how it differs from the ones that you are talking about but as you said I know that they aren't compatible with normal stats) In fact we just realized we underspeced the tonnage and have to now replace our 3.5 ton compressor with a 5 ton (yay money to spend!) and expand our main trunks.
The term HVAC techs use is "communicating" thermostats. They are proprietary, but not necessarily closed-off from automation. I have a Daikin (aka Goodman) unitary variable speed and variable valve gas heat with variable speed condenser. I can control it via a community created driver via HTTP. Whether any specific communicating system allows automation is up to each manufacturer. So do your homework first.
That is great; I hear that Daikin is a good brand. I have a Carrier Infinity right now and only Amazon or Google can connect to it. I am going to pull it out and get a single speed Goodman 16 seer with a matching blower. I will then put in an Ecobee.
You probably have the two speed Goodman. If the thermostat is not set up for Y1 and Y2 it will run in the lower speed mode all the time. Check that before you upgrade. If you do upgrade by the single speed 16 seer Goodman. It is rock solid and can be fixed by any companies parts.
P.S. The Thermostat wiring must go all the way to the furnace and the furnace wiring must go to the compressor with the additional Y connector. If at any spot you are missing the Y2 it will only operate in the reduced air mode.
Great. It is worth opening the furnace and seeing that it is connected there. I have automated a lot of homes and when I replace the thermostat on 2 stage units almost half the time I notice this. You can make sure that the two stage is working on the compressor by ear. Go to it when it is in normal low (almost meeting temperature) and then have someone lower the temp by several degrees while you stand by the compressor. It should make a lot more noise in the second stage.