Hi there, Griffin,
I see from your post that you're having trouble with the AirPods charging case. It's charged, but won't turn on unless you plug it in. Then, you see a flashing amber LED until you remove the AirPods and place them back in, and then you have to pair the AirPods with your phone again. I'm happy to help!
This can happen if your AirPods are from different generations. While you can use both generation of AirPods with your charging case, the AirPods themselves must be from the same generation. If you're not sure, you can use Identify your AirPods - Apple Support to help determine if your AIrPods are from the same generation.
If they are and the issue continues, it might be because they have different firmware versions. To solve this, place both AirPods in the charging case and close the lid. Then, connect the charging case to its charger for 20 minutes. After 20 minutes, hold the set-up button for up to 15 seconds until the LED flashes white, then set them up with your iPhone again.
If you're still having trouble after that, you'll need to speak with Apple Support directly, which you can do here: Contact Apple Support.
Cheers.