ETA, kind of a good news update. As an updated to what I posted below at first, it DOES look like even the annotations created on personally added docs (side-loaded books into your cloud Kindle account) in smart devices (android, iOS) running Kindle, actually get synced to the Kindle e-ink device as well. Updated inline to reflect that. In short, the impact of that is: Amazon's Kindle cloud account is the ONLY free and easy-to-use option I know of for converting books purchased elsewhere into Kindle format, uploading to your cloud account, and syncing books/highlights/annotations to ALL device types (e-ink, Android, iOS, PC).
Personally added ebook files to the Kindle cloud (such as an epub purchased elsewhere, and De-DRM'd) do sync across devices, at least for me they do. It gets a little tricky like I said abovebut it still works. I just ran a quick test with an epub and confirmed book syncing across devices for an uploaded epub still works.
* One caveat to note: the Amazon cloud notebook that shows annotations on ordinary purchased Kindle books, does NOT show annotations created on personal documents. The annotations you create in a sideloaded book, regardless which device you use, DO get synced to all the devices but those notes are simply not synced in the Kindle cloud notebook. Therefore, to extract and backup notes on sideloaded books you've added to your Kindle cloud, you can use Calibre to import the annotations. Or you can get various 3rd party apps to extract the notes to things like OneNote, PDF, Excel, markdown, or Evernote. Two such examples are the Knotes app, and the
Snippet app.
With all that said, the Kindle platforms support for syncing 3rd party ebooks and their metadata across devices for free is, IMHO, far and away better than any system available . And that's why I use it rather than say, Google Play.
If OP interested in using this approach, here's what I do to get a 3rd party book such as an epub purchased elsewhere, into my Kindle devices/apps:
1. Setup your Amazon Kindle account by going into settings, and enable Personal document archiving, and find out what your send-to-kindle email address it.
2. Download and install Calibre, and the Alf DeDRM extension. There are threads and folks here at Mobileread that can help if you have trouble doing this.
3. After you buy an epub book, use Calibre + Alf to DeDRM the book.
4. Make a local copy of the DeDRM'd epub file, and change the file extension to something like ".png". So your file name would look like MyEbookFile.png.
5. Email the file as an attachment to your send-to-kindle address that you got out of your account settings.
Now Amazon converts that epub to their format, the ebook appears in your "Personal documents" in your Kindle account. The book file will sync to all your devices. Annotations should sync as above. To backup your annotations out of your sideloaded books, I'd use in this order: Calibre if possible, or the Snippet app.