You can use both Wi-Fi and Ethernet, just rearrange the interface order in system preferences and your networking will all go through Ethernet and all these features will use Wi-Fi.
This is surprising. What's in a WiFi connection that is not there in an Ethernet one?
Do they ignore the home network and communicate directly WiFi card to WiFi card?
It's probably based on AWDL, same as AirDrop. So yes, that's a proprietary peer-to-peer protocol that ignores your home network.
If you disable automatic connection for that network, you can have Wi-Fi on without being connected (I have this setup on a work Mac connected via Ethernet so I can use AirDrop).
You don’t even need to do that, just rearrange the interface order.