I‘ve got an iPad Air gen3, latest iPadOS, but the AppStore won‘t load down the fitness app.

Hi, and welcome to the Apple (user-to-user) Community!

Re: AppStore won‘t load down the fitness app : Any idea, what to do?

Check that you are signed in (to your iPad) with your Apple ID:

Sign in with your Apple ID - Apple Support

Also:

Apple requires you have a payment method listed in your Apple ID account for the first time that you use, iTunes or the App Store, even if you are only downloading free apps.

Payment methods Apple can accept in your country or region:

Payment methods that you can use with your Apple ID - Apple Support

How to add an Apple ID payment method:

Add a payment method to your Apple ID - Apple Support

How to delete an Apple ID payment method:

Remove a payment method from your Apple ID - Apple Support

Else: What to do: If you can’t download or update apps on your iPhone or iPad - Apple Support

Or If needed:

App Store Support website (info. / support / contact):

App Store - Official Apple Support

All the best :-)