Microsoft Edge is finally getting the History and Open tabs sync feature with Chromium Edge version 88. As the feature is currently rolling out to a limited set of Edge Insiders in the Canary channel, you can now see the options to enable the sync if you are one of the lucky users.
The feature is currently rolling out for Windows, and Mac users. Upgrade to Edge Canary build 88.0.682.0 or higher to check if it has been enabled for you.