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.