I'm not suggesting changing the default browser... only that given some of their past actions, simply putting the icon, or updating the version of Edge on the taskbar, and having a notification above that icon would be a better approach. Compared to the suggestion that disparages Firefox or Chrome, or the full browser window opening after the update.
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It's easier to unpin a taskbar icon, than disable suggestions.
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It's easier to unpin a taskbar icon, than disable suggestions.