Want to give a shout out to Asus. Their AiMesh ecosystem seamlessly handles adding nodes with/without Ethernet backhaul. I had a TP-Link extender and switched due to the TP-Link having only 100Mbps Ethernet. Not all TP-Link range extenders do this, I wrongly assumed since it claimed 600 Mbps wifi speeds it would include 1 Gb Ethernet. My bad.
The big issue was how easily the Asus router accepted the Asus node into the fold. Night and day difference in ease of configuration.
Not sure why the OP is logically separating mesh nodes from range extenders. Just have to put a mesh node inside the transmission radius, and voila, your range is extended.

