Here is some more info...
The access point spanned by the Carlinkit adapter only offers 802.11n 2x2 40MHz @ 300mbps:
View attachment 1767023
It uses channel 36 which is UNII-1 and not the advertised 5.8GHz band (UNII-3). This should make any difference though.
Apple actually recommends 802.11ac VHT (using up to 80MHz wide channels resulting in 866mbps) and even mandates WMM. The Carlinkit 2.0 adapter offers neither despite the built-in Realtek WiFi chipset supporting both. I don't know whether it would make much of a difference since CarPlay is a point-to-point connection, not using a hell of a lot of bandwidth anyway. It might however bring down latency.