Apple TV Ethernet Connection with Wi-Fi Features

In a word, nope. When you plug in the Ethernet cable, that makes an Apple TV only able to connect via Ethernet. If you unplug the cable then the Apple TV will connect (or try to) connect to a Wi-Fi network. You cannot get partial features of a network connection type when using the other, meaning its Ethernet or Wi-Fi and that's it.

Any way to have the Apple TV plugged into via ethernet but still have the wifi capability …

It is one or the other. But that shouldn’t be an issue. A good router would have the ability to combine both network segments as one logical network. Most consumer models would even default to that. You would lose that function if you define separate SSID network names for Wi-Fi bands (2.4 GHz, 5 GHz) though, so don’t do that.

Recommended settings for Wi-Fi routers and access points - Apple Support

… to allow find my remote, airplay and the remote app to work?

These functions work for me on Wi-Fi as well as ethernet. It is in your router settings, not in Apple TV.