AirPods only connect when charging case is plugged in

Hi StarCrap,

We appreciate you reaching out to us.

We recommend that you reset your AirPod Pros if they are not working as expected.

1. "Put your AirPods in their charging case, and close the lid.
2. Wait 30 seconds.
3. Open the lid of your charging case, and put your AirPods in your ears.
4. Go to Settings > Bluetooth. Or go to Settings > [your AirPods]. If your AirPods appear there as connected, tap the More Info button  next to your AirPods, tap Forget This Device, then tap again to confirm. If your AirPods don't appear there, continue to the next step. 
5. Put your AirPods in their charging case, and keep the lid open. 
6. Press and hold the setup button on the back of the case for about 15 seconds, until the status light on the front of the case flashes amber, then white.*
7. Reconnect your AirPods: With your AirPods in their charging case and the lid open, place your AirPods close to your iPhone or iPad. Follow the steps on your device's screen."

You can use the article below as a reference.

How to reset your AirPods and AirPods Pro - Apple Support

If the issue continues, please perform another reset and then pair your AirPods Pro with a different supported device.

If the issue persists while your AirPods Pro are paired with a different device, please use the link below to explore your service options.

Get Support

Take care!