That's not how it works. The Green acts as a hub, and a wired connection to the network is less prone to interferences and other disruption that could put the brain of your smart home, offline. Wireless connectivity should be provided by the network's router (which, these days, almost all provide it), giving esphome devices a mean to connect to the network and reach the Green.

For what its worth, I'm still on 6.15.3-12 but 6.16.2-88 has just been made available to me. It wasn't when I checked 12 hours ago. Maybe third time's the charm.