Whether you need a router is really a question for Verizon. Their website (https://www.verizon.com/5g/home/) says a Wi-Fi 6 router is included.
I would think that, as far as your Nest thermostats are concerned, Verizon 5G internet service is just another internet service provider. We don't have Nest Wi-Fi, so I can't speak to the technical aspects of connecting Nest Wi-Fi to a Verizon router.
I just wanted to jump in real fast to see if you saw MplsCustomer's reply and to see if you still needed some help on this or if you were able to get it sorted out. If you are still needing some help, just let us know and we'll be happy to continue helping.
I wanted to follow up and see if you are still in need of any help. Please let me know if you are still having any concerns or questions from here, as I would be happy to take a closer look and assist you further.
Just one quick final check in here since activity has slowed down. We'll be locking the thread in the next 24 hours, but if you still need help, I would be happy to keep it open. If there's more we can do, just let me know.