How do I manage books on my phone that I did NOT get through Apple?

This is has been a huge problem for me ever since iTunes dropped ebook support. I've picked up a lot of free (fully legal) ebooks from various sources, some of which I've downloaded directly to my iPhone and some of which I originally downloaded to my PC, and it's gotten harder and harder to keep them usable in the Apple Books app. (The books are not available directly from the Apple Store.) At this point, I'm even delaying an upgrade to a new iPhone because I've discovered that these dozens of ebooks will not be included in my backup and therefore will not transfer to the new phone. It seems impossible that something iTunes used to do natively is now just...not an option in any way.