the google TV is probably your best bet without either breaking the budget or buying questionable off-brand android boxes (many of which have been fount to have malware included)
You can indeed add a usb-c ethernet adaptor if you have a pass through power USB-C hub/breakout, or the simple solution is to buy the official chromecast ethernet adaptor that is integrated into the power supply. they are available from Google directly, or compatible knock offs are on amazon.
Total cost of that rig of dongles and adaptors is still significantly less than an NVIDIA Shield, even the basic tube model.