trying to send proof of purchase to check warranty

Send it to where?

Enter your serial number here to verify your warranty: link-> Check Your Service and Support Coverage - Apple Support

If you need to update your proof of purchase, then follow the steps in the support document you came from to contact Apple Support by phone. They will tell you what you need to do to update proof of purchase.

Yes, you need to contact Apple Support as explained in the support document you came from. They will tell you what you need to do s to send them proof of purchase.

Please read the support document you posted from.