From what I’ve read, most ereader/app pairs only sync if you buy them from the respective store.
They might have a feature to upload books to their cloud. These books would then sync between their devices and apps. For example, Kindle ecosystem has a feature called Send to Kindle that can do that. The easiest way to use it is to use the web app (https://www.amazon.com/sendtokindle) on computer: You just drag and drop files to that page, and they are added to your Amazon account.