If you really need to cheap out on it, you can remove the wireless chip from an existing RC car and take over the H bridge inputs, or even just tap into the antenna input pin and inject serialized commands.
Most low-end 27MHz toy RC sets use clones of a well known chipset called RealTek TX2/RX2, and there are Arduino libraries for it. It only takes binary on/off commands for forward/back/left/right/"turbo" at 1Hz or so, which is fun enough for most purposes.
I put a link above for this kit which is about $50. However, I believe you would also need an ESC for the motor, a suitable one would probably be less than $20.
Hi, thanks for the feedback. I have updated the README with the materials I used:
I bought everything for this kit from aliexpress:
Car chassis: https://www.aliexpress.com/item/32830665408.html Electronic speed control: https://www.aliexpress.com/item/1005007716682815.html Battery holder: https://www.aliexpress.com/item/1005006283625827.html 2 18650 3.6v cells or 7.4v battery pack (I have used both, cells are more flexible for other projects) ESP32-CAM: https://www.aliexpress.com/item/1005001468076374.html (Very important to get one with external antenna and and I used the 170 degree fisheye camera) Bluetooth Gamepad (I used a PS4 controller)