I have original Chromecasts running on both wired network and wifi, and I have wired Android TV’s. Wired network should not make a difference. As long as the new Chromecast is compatible with older chromecasts it should be supported.
I don’t know how you used it with wired Ethernet, the old dongle for Chromecast can probably not supply h power to the Chromecast device due to more powerful hardware. You also should not power it through you TV set but with the original adapter. I understand there is an official ethernet adapter, that should be fine but isn’t sold where I live.
Eiter way I reccomment you supply the Chromecast device with a fixed IP address.
I understand the new device is more based on android tv than is is on the original Chromecast. Then it most likely has a “Chromecast built in” service. Have you tried downloading updates for all apps to see if this service has an update too? That might help.
You say you can see it now, but that it doesn’t help. What exactly do you mean by that? Where you able to add it as a Chromecast to Homey? You shouldn’t expect more from it than e.g. a Nest Hub.You can cast to it, but it won’t do much more than control the volume of the Chromecast. It will not help you control your actual TV.
Also, Android TV is even more limited than a standard Chromecast where it comes to controlling Netflix. This is not a Homey problem, it is e.g. also not able to start a Netflix show using Google Assistant. I expect Google TV to be equally limited. This is because Android TV does not actually cast Netflix to it the traditional way, but instead opens the Netflix app on the device and casts to that so you’ll have the full on screen Netflix experience. Basically you’re remote controlling the Netflix app itself.