Thanks for replying, Mellie13, and that additional info, it really helps! Let's make sure you have followed the steps Apple recommends when there are CarPlay issues:
1. "Check your connection to your CarPlay stereo:
* If you have a wired connection, try connecting again with a different USB cable to a different USB port if you have one.
* If you have a wireless connection, make sure that Bluetooth is turned on on your iPhone under Settings > Bluetooth. Then go to Settings > Wi-Fi, and make sure that Wi-Fi is also turned on. Tap the CarPlay network, and check that Auto-Join is turned on.
4. If CarPlay doesn't activate automatically, look for the CarPlay logo on your car's display and select it.
5. Restart your iPhone and your car.
6. Make sure that Siri is on.
7. If your iPhone isn't detected by CarPlay, make sure that CarPlay isn't restricted. Go to Settings > Screen Time > Content & Privacy Restrictions. If Content & Privacy Restrictions is on, tap Allowed Apps, and make sure that CarPlay is enabled.
8. Go to Settings > General > CarPlay, tap your car, then tap Forget This Car. Then set up CarPlay again.
9. Make sure that your CarPlay stereo is using the latest firmware from the car manufacturer. Check your car's manual for more information.
If you still have issues connecting to CarPlay, contact Apple Support."
And those steps are from If you need help with CarPlay - Apple Support
After you have Hyundai check for updates for your car stereo, if you are still having issues, please contact Apple directly for further investigation: Get Support
Have a great day and thanks for using the Apple Support Communities!