Perhaps I misread your original question. When you asked how, did you mean how do you get Kindle books off of an iPad for backup?
If that’s the question, to best of my knowledge the answer is that you don’t. So far as I know, that just isn’t possible.
Yes, I’m afraid that is the way it is 
You can go to the website and download them to the files app. But you cannot do it from the Kindle app.
When I try to do that on my iPad, I get the message that I do not have any compatible registered devices.
I’ve been downloading my content regularly for a long time, so I didn’t have to download very many books in the last week to have my collection up to date. And I have an e-ink Kindle, so once books are on that device, it’s easy for me to get them from the Kindle to the computer. So I’m all set.
But my inner nerd is very curious about how you did this on an iPad. 
Once this feature goes away, you’ll still be able to manually copy ebook files and other documents to Kindles over USB using Amazon’s apps or third-party solutions like Calibre. You just won’t be able to download copies of your purchased books to a computer.
Yes, but I think the issue is this? (from the same article)
Amazon has occasionally removed books from its online store and remotely deleted them from Kindles or edited titles and re-uploaded new copies to its e-readers.
…
t’s a reminder that you don’t actually own much of the digital content you consume, and without the ability to back up copies of ebooks, you could lose them entirely if they’re banned and removed.
That’s why I wanted to make a local backup of my purchases (rentals?).
Licenses. You’re licensing the ability to read a copy you’re licensed to. Amazon has the ability to revoke that license.
I can accept the licensing issue (sort of) BUT no access to Libby and recommendations (read Ads) dominating my Home Screen have me seriously considering discarding my Kindle and digital books in general.
In Australia, there is no mechanism to read books through Libby on a KIndle. Advice from my local library:
“Currently there is NO Kindle eBook lending platform available to Australian public libraries. Without it being available, we simply cannot offer such a service. The owner of Kindle (the US company Amazon) currently does not allow Australian Kindle owners to access the few eBook/Audiobook lending services that Australian public libraries are able to subscribe to.
The Kindle is a proprietary product sold by Amazon. It uses its own particular software & Amazon is keen for Australian Kindle users to purchase their books through the Amazon store” of course they are. That said, Apple Books has its own restrictions but at least the IPad allows other apps like kindle, Libby, overdrive etc. And yes there is the Kobo, but that just locks you into another propietary system.
So with the public library limitations, the restrictions on how I can share my books with family, and recommendations being shoved down my neck, make me think - why bother? Perhaps just buy paper books and then hand them on to others once read.
Of course there is a question of carbon footprint with that method and I am not sure what the digital vs paper carbon footprint calculus is)
Or I can just squander my days watching WWE…(no criticism - it is entertaining theatre in limited (15 minute) bursts…or worse, some ill informed current affairs pap…