Hi Lockersc,
The following is from the support article Use CarPlay with your iPhone:
"Make sure that your stereo is in wireless or Bluetooth mode. Then on your iPhone, 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. Then, go to Settings > General > CarPlay, and select your car. Check your car manual for more information."
Also, If you need help with CarPlay indicates "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."
Based on these articles, it would appear that Wi-Fi is utilized or necessary for the CarPlay connection. Some radios offer a Bluetooth-only connection for audio playback which is not the same as CarPlay per How to connect your iPhone, iPad, or iPod touch to your car.
You may try using CarPlay via a cabled connection and test if your Wi-Fi options with the other accessory are then functional.
Regards.