Add a "Fetch All" option to the Repositories context menu (alongside "Add Repository...", "Clone...", "Rescan Repositories...") that fetches all repos in the manager—not just open tabs.
After fetching, show an indicator icon on repos that have incoming remote changes, so it's easy to see which ones need attention without opening each tab.
This would be "simpler" that a similar request for Windows: fork-dev/TrackerWin#2140