I downloaded a non-Apple epub on my iPhone running IOS 16.0.2. I then opened Files and the Download folder and tapped the newly downloaded epub. It opened. Closing the file showed it as the most recent addition to Apple Books (which I confirmed by opening Apple Books on my computer).
There are a wide range of EPUB 3 reading apps available and the reading app evaluation available at epubtest.org helps the reader make the correct choice for them giving them the best access to their downloaded documents. There is also a quick roundup of these results on Inclusive Publishing to help beginners get started. 2b1af7f3a8