I can’t download the fitness app on my new iPad Air 4 and I’m currently running iOS 14.4

Your iPad needs more that just the app.

Your iPad needs to be updated to the latest iPadOS 14.3 or later.

You need a compatible Apple Watch ( series 3 or later ) updated to its latest WatchOS version and, also, Bluetooth connected to your iPad before the iOS App Store will let you download/install the Apple Fitness+ app.

You need to have or purchase an Apple Watch series 3, or later.

No options.

Also, make sure all connected Apple devices are using the same Apple ID/password account information.

In addition, there is no TV mirroring of the Apple Fitness+ app, using iPad, currently.

Currently there is no direct AirPlay/screen mirroring from an iPad to any other compatible smart TV or smart device using AirPlay2.

Apple, currently has ONLY made the mirroring/AirPlay 2 feature available to owners/users of an actual Apple TV box.