Hello, I understand you are having issues with your purchase of a CT100 thermostat, since it’s not running your heat. The key to this issue is a dual fuel relay kit; optional equipment on many thermostats, which an HVAC usually will configure to shut one system off depending on ambient temps. Your installation looks like it would work with just an outside temperature sensor location on the stat. The CT100 and Trane TZ400BB3VZNNSL both have this, but their instructions say to tape this lead off, which is probably what your HVAC tech was trying to convey to (national alarm franchise omitted) installer.
We have a 'sister' to the Trane TZ400BB that looks like it would work for you. It has provisions for multi-stages, and screw terminals for installing your outside temperature sensor - American Standard AZEMT500BB32MAA.In the meantime, I would pass this information (national alarm franchise omitted) and your HVAC tech, to see if they agree that this will work for you.
In particular, look at pages 4-7 to find the appropriate wiring diagram that fits your air handler and heat pump, AND Page 8 that describes how to wire the external temperature sensor AND Pages 10-12 to configure the stat to your system + add the correct outside sensor configurations. Once that is complete, there are instructions on how to add the thermostat into your (national alarm franchise omitted) system.
Now that I think about it, since this is all absent from the various other stats I have searched through, I guess the interface doesn't have this built in on certain models of the others, which is why the wires are there but they say to tape them off.