Why isn’t my Nest thermostat listed under Home.

The Nest thermostat is not currently compatible with Apple’s HomeKit. Google owns Nest. Read the following article about Google’s plan to support HomeKit.

https://www.cnet.com/home/smart-home/google-nest-to-integrate-with-homekit-bringing-smart-home-unification-one-step-closer/

For you to think about, there are a number of home automation systems out there that are not compatible with one another. The big players like Apple and Google, Amazon have been working on a universally compatible connectivity system called Matter. It’s not here yet though.