do I have to buy Apple CarPlay?

Apple CarPlay is built into iOS and your iPhone. You don’t have to download it and there is no charge to use it.

How to connect your iPhone, iPad, or iPod touch to your car - Apple Support

Follow the instructions in the like provided. Be aware that there are two types of connections, wired and wireless. Check the owners manual of your Hyundai to see if it supports wireless CarPlay.

CarPlay is included in iOS and has been since iOS 7?, so about 10 years now.

There are two versions, one only works with wired connections (so your phone has to be plugged into the car's USB port), the newest versions work wirelessly. Wired or Wireless depends on the specific car model you have, not the phone.

As for how to set it up, that's up to the car itself, but in my (non-Hyundai) experience, when you first connect the phone (either wired or wireless as appropriate), you're asked if you want to start CarPlay or not.

Either way, there's no charge (beyond having a phone and a car, of course :) )