The highlights for personal documents (stored in user's Kindle cloud, using send-to-kindle etc.) do sync. But the desktop apps cannot access personal documents in the cloud and those highlights. They will sync with Kindles, just not with Kindle apps that don't support personal documents (Windows and Mac OS).
If you side-load documents, the annotations won't get synced, of course.
If you want to get your annotations from personal-documents-in-the-cloud, that is (relatively recently) possible. But you have to use the Export Notes feature that exists in the Kindle apps for newer Fire tablets on Fire OS 5, Kindle for iOS, or Kindle for Android. When reading personal documents on a Kindle, the Export Notes feature is not enabled.
Kindle.amazon.com is still there, but it only works with amazon content and is a poor alternative to the export notes feature (supported in recent Kindles, Fires, iOS and Android).