Probably due to a poor implementation of hotspot by the car. Car Play uses a combo of Bluetooth and WiFi, with the connection starting by using Bluetooth to make the WiFi connection.
Traditionally, hotspots like those sold by cell phone companies use 5G or 4G cellular connections and create a local WiFi for devices to connect, so the devices can use the local network to communicate with each other (peer to peer), and the cellular router for internet access. If Hyundai didn't do this right, they may be opening a route to the internet only, and not allowing peer to peer local connections (phone to head unit).
My home uses a TMobile 5G home internet service (which is very much like the Verizon Hotspot in the car), I connect to the hotspot (modem/router) via WiFi and can connect to all of the other computers and devices in my home as well as to the internet. That is how the car hotspot should work, so if Hyundai went cheap with a cellular hotspot that routes everything through the WAN (internet) port, it would fail to make the local connection to the infotainment system. Underlying all of this are network scripts that define routing rules. For instance, on a normal home router, it would say anything with an IP Address in the same private subnet (typically 192.168.x.x) as the sending device (phone) would not go out the WAN port, and everything else would use the WAN port. I suspect Car Play uses Apple's Airplay (Bonjour) routing protocol, which is not routable.
The reality is, the car's hotspot really doesn't solve much for modern smartphones with unlimited data plans. About the only benefit is the car's hotspot has a more powerful radio than phones, so might pick up a better signal in fringe areas.
Your choice may come down to turn off the car's hotspot indefinitely (and don't subscribe with Verizon going forward), or use USB for Car Play.
