I was the lead engineer on a mesh wifi system. Not only do I recommend mesh WiFi, but I high recommend you throw your extender in the garbage. Many extenders cause wireless interference, which will actually make your quality of connection worse on both networks. They are essentially a second WiFi network in your house. Some smart ones will put you on the same subnet so your devices can communicate with each other across networks, but the router and extender will not tell your device when to switch from one network to the other. This will mean that whichever one your phone connects to first, it will stubbornly stay on until you either turn your wifi off and back on on your phone, or your phone's wifi connection is so horrible that it can't communicate at all. This is what mesh does well. It sends a message to your phone saying which node you have the strongest reception to, and assuming your device supports mesh AP steering (most phones made in the past decade do), your phone will automatically hop to the node with the strongest signal as you walk around your house.

The price of mesh networks has come down dramatically since it first got popular a decade or so ago. Ideally, you could have a wired connection between nodes, but it isn't required. You just may need more nodes to make sure they all have a strong connection with each other. Remember that mesh nodes are going to have much larger antennas than your cell phone or laptop, so they will be able to get decent reception in a spot that your phone might get just okay reception.