I did look into that, but it means installing another app from what I've read (meaning I'd be just switching from the Trane to the Home Assistant one). If it allows me to control the thermostat from Apple Home, I'd be for it.

Once you get Home Assistant to control your thermostat, you can add the excellent HomeKit integration to HA. That exposes all or some of your devices in HA to Apple Home. You can then access them like other Apple Home devices, including via Siri if that’s interesting to you. It’s great.