Do Wi-Fi extenders slow down your internet?

Usually yes. Consumer Reports and specialist communities such as r/HomeNetworking repeatedly note that traditional single-radio extenders roughly halve your throughput because the device talks to the router and your devices on the same radio. Dual-band and Wi-Fi 6/7 models with a dedicated backhaul band and a wired Ethernet uplink mitigate this, which is why reviewers favor models with a Gigabit or 2.5G Ethernet port.