At some point, it becomes economically unfeasible to support older operating systems.
Zwift made an announcement about changes to OS support, here: Upcoming Changes to Supported Operating Systems [Effective August 2022]
If you’re using the original iPad Air from 2013 (an 8 year old device), Apple elected to stop providing iPadOS updates beyond version 12 so it is affected by Zwift’s OS support change.
@Dave_ZPCMR pointed out in that thread these minimum device specs needed:
As for cost of newer devices, Apple sells refurbed (with warranty) 7th Gen iPads for 249,00 €: iPad Wi Fi 32GB ricondizionato Grigio siderale settima generazione - Apple (IT)
EDIT - AppleTV4K 2nd gens are 169,00 € Apple TV 4K 32GB (seconda generazione) ricondizionata - Apple (IT)
Frankly, the used iPad market is kind of bonkers so you could even sell your iPad Air 1 to offset the cost of a newer unit - people pay way too much for them, which could work out for you.