With iOS 13 and iPadOS 13 Apple introduced a new way to download and save files on your device within Safari.
Once you select download you will see the download indicator appear and start to download your file. The download indicator icon is located in the upper right, next to the web address.
To access the DOWNLOADS folder, touch the download icon, located in the upper right, next to the web address. Touch the downloaded epub file to open in your default ereader. (Typically the default ereader is iBooks on an iPhone or iPad).
