£566 is a lot for a battery.

It’s £92.44 for a battery
https://support.apple.com/en-gb/ipad/repair/battery-powerNot for an original 12.9 inch iPad Pro it ain’t. Mine popped about 2 days after the apple care expired and Apple tried to charge me £566.
https://support.apple.com/en-gb/ipad/repair/battery-power
£92.44 for all models. It either needed more work or they got it wrong.