Apple tv is extremely slow and sluggish through my remote and iphone app

Check your HDMI cable! It causes interference if it is a poorly shielded cable

I’ve had a similar issue lately — my Apple TV started lagging a lot when navigating menus, even with the iPhone remote app. What helped me was restarting both the Apple TV and my router, then turning off Bluetooth devices nearby (they sometimes interfere).
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If your Apple TV is slow or unresponsive, restart both the device and your router, then clear cache-heavy apps or reinstall problematic ones. Also, check for tvOS updates and disable Bluetooth accessories or AirPlay connections that may be overloading the system.