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Microsoft has just begun pushing out its new Edge browser update, which adds history and tab sync to the browser going into 2021.

The roll out of the new Edge features will spread throughout the world over the coming weeks, but if you want to see if you've got it already then visit Settings > Profiles > Sync and then enable "History" and "Open tabs" for the new Edge abilities.
Edge launched back on January 15, 2020 -- if you can believe it, it feels like longer than that -- launching without a Sync option... for some reason. Microsoft launched Extensions in May 2020, promising the history and tab sync would be here by the end of the year but they didn't make it.
They're here now, and should be rolling out in the coming weeks worldwide to Edge browsers.