I, too, have the Carlinkit 4.0 adapter. Works very well for me overall, only had a couple times where I needed to unplug it to restart it and get things going.Definitely worth the price. I'd say that there is an extremely slight lag between when you select something for the change to happen, but not nearly enough to be annoying, imho.
https://carlinkitcarplay.com/products/carlinkit-wireless-adapter-for-factory-carplay