TP-Link AC1200 Gigabit WiFi Router (Archer A6) - Dual Band MU-MIMO Wireless Internet Router, 4 x Antennas, OneMesh and AP Mode, Long Range Coverage

That extender can't be connected to the incoming network cable from the house. It only connects via a wifi signal from another wireless device. You can use something like this router in access point mode for low cost. https://a.co/d/0bwdgshJ

You plug the current ethernet cable from your pc into the WAN port of the new router and get another lan cable (normally every router you buy has one included anyway) to connect the pc to a free lan port on the router. Then when setting up the router, chose AP (Access Point) Mode (or Switch Mode, some call it that way) Best pick for your budget, but a bit over your budget: https://a.co/d/0ezDk42I Else a normal 5ghz router which does the job just as good: https://a.co/d/02c4xFny