Should I repair my ipad or should i get a new one?

Your fourth generation iPad Air can run the most recent version of iPadOS - and as such, there is perhaps no pressing reason to replace your iPad at this time. That said, the Air4 does not support the Apple Intelligence features introduced with iPadOS 18.x.

For practical purposes, in lieu of replacing the battery and returning your own iPad, Apple usually exchange the iPad for a renewed/refurbished iPad of the same model and specification. The cost of the exchange is the same as would otherwise be charged for battery change - and benefits from having an additional limited warranty.

As for costs, Apple offers a fixed-price price battery replacement. You can verify eligibility and cost for your region/country here:

iPad Repair & Service - Apple Support

If you have an active AppleCare+ plan, the cost of repair is reduced to a small excess/deductible fee.

...but the battery is inflated,

A swollen battery does extensive physical damage and I doubt that you will be able to take advantage of the US$119 battery service. If the battery has damaged anything else, you fall under "Other damage" and the cost skyrockets if you do not have AppleCare+:

Also, you cannot take advantage of Apple's excellent ship-in/mail-in service because you cannot ship or mail a device with a swollen battery.

I believe you will be better served by replacing this iPad.

iPad Repair and Service - Apple Support

The rest is up to you to decide if you should purchase a new one or not.