Nest Thermostat will not connect through Matter, HomeKit or another platform

The checks in more detail

The phone must be on the same Wi-Fi as the thermostat, Bluetooth must be on and the thermostat must be online. Apple Home needs a home hub, an Apple TV or HomePod, for remote control. If the option is not offered, the thermostat's firmware or the Google Home app may need updating, or your region may not have the feature yet. A Matter device already paired to another controller must be shared through multi-admin, not paired again from scratch. If pairing fails, restart the thermostat from its Reset menu and try again, make sure the Google Home app is updated and look at the thermostat's firmware version in Settings.

Do not remove the thermostat from Google Home to add it to Apple Home, since it needs to remain in at least one ecosystem. Once linked, the thermostat appears in Apple Home as a thermostat with heating and cooling modes and a target temperature, but some features such as Eco modes and Home and Away assist stay in Google Home. If commands are slow, the path goes through the home hub, so check its connection. Keep the thermostat on a strong Wi-Fi signal.

If you use voice assistants, a command that works in Google Assistant may not have an equivalent in Siri, so test each. Use Apple Home's automations carefully with a thermostat, because a mistake can leave heating on. Matter support on thermostats is still developing across platforms, so it is worth checking whether the feature you want, such as setting a temperature by voice in Apple Home, is supported before spending time on setup. If the thermostat appears in a platform but shows an error, remove it there and add it again with a new pairing code from Google Home.