Hello Paul! Using the Apple TV 4K (2021) and the actual model Eve Door & Window will give you a bit more range compared to Bluetooth. But in difference to Bluetooth you may expand the network using a powered Thread enabled accessory 'half way. This could be an Eve Energy (EU/US/UK) or a Nanoleaf Essential bulb or light strip.
As of today the Nest product won't. This may change within the next year with Matter but ne information so far, sorry.
The current generation of Eve Motion is not ready for Thread. We will be releasing new hardware generations of many Eve devices with Thread support later this year, but unfortunately can't give any further details on when this will be the case for Eve Motion at this time.
Here's a list of all the currently available Thread-enabled Eve accessories:
Best regards, Volker
Jul 7, 2021