Battery issue with my iPad Air 2

Your iPad Air2 is considered to a be a “vintage” product (defined as being more than five years, but less than seven, since the end of production. For “vintage” devices, repairs and battery replacement are possible subject to availability of parts.

Devices that are older than seven years from end of production are “obsolete” - and are no longer supported by Apple for hardware repair or battery replacement:

Obtaining service for your Apple product after an expired warranty - Apple Support

If your iPad Air2 was “rejected” per your description, this would suggest that either parts are no longer available - or your iPad has some other damage or fault that precludes eligibility.

Genius Bar Reservation and Apple Support Options - Apple

iPad Service & Repair - Apple Support

You can pay to get the battery replaced. However given the age of your device you may find the money is better spent going towards a new device instead of replacing the battery in an older model

iPad Service & Repair - Apple Support

it's just too old to be replaced at this point, consider purchasing a new iPad or buying a used one