How do I connect Apple tv 4k 2022 to Nest Pro Wi-Fi mesh router using 6.0GHz band?

Wi-Fi 6 is not the same as Wi-Fi 6E. Only Wi-Fi 6E uses the 6 GHz band. Apparently the Wi-Fi Alliance had to get the 6th version standard out before 6 GHz could be included.

Apple TV 4K (3rd generation) technical specifications - Apple Support

Wi-Fi 6 (802.11ax) with 2x2 MIMO

So the specs are at least ambiguous about it. I’m not convinced that the 6 GHz use is included. I think they would have said so if it did.

Wi-Fi 6 - Wikipedia

IEEE 802.11ax, officially marketed by the Wi-Fi Alliance as Wi-Fi 6 (2.4 GHz and 5 GHz) and Wi-Fi 6E (6 GHz), is an IEEE standard for wireless local-area networks.

Thanks for posting in the Apple Support Communities 123Luckie,

The following steps may help refresh the connections between your devices:

Restart your Apple TV, router, and modem

After you restart each device, see if you still need help.

On the Apple TV menu, go to Settings > System and select Restart.

Unplug your router and your cable or DSL modem from power. Then plug them back in.

You can find these steps, along with additional guidance that may help you reach a solution, here: If your Apple TV can't connect to Wi-Fi

Cheers!