You would grab a SmartThings Hub and connect it to your WiFi
or, to replace your current WiFi router, grab a
SmartThings WiFi 3 pack(if you need more coverage)https://www.samsung.com/us/smart-home/smartthings-wifi/multi-packs/samsung-smartthings-wifi-3-pack-e...
Set them up with the wizard in the SmartThings app, and you can connect lots of [Z-Wave\Zigby]sensors and products to SmartThings, and use the app to automate all of it.
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How do you backhaul to the extra hubs through the ethernet? I've got 5E running everywhere I'd put a hub, which should be sufficient for my needs, but the instructions only show how to connect these pucks to each other throught wifi.