I don't use Kindle Desktop--at all--so I can't answer the Q on that app.
However, it's definitely the case that you can sideload epub books into your Amazon cloud as a "personal document." I use Kindle-for-PC app for that purpose, though they do have other options like email conversion. Then if you add annotations to sideloaded personal documents on your devices that connect to your Kindle account (iOS, Android, Kindle), the annotations will sync across those devices. I do this all the time. If you set it up like I've suggested here with your devices, would be interested to hear if you find that it also syncs successfully to the Kindle PC desktop app.
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