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Instead of the current logic which is "Check for updates once at launch, if it has been either over 6 hours since the last successful check OR the time of last check is in the future.", the update check/update download should happen every six hours in the background, and the user should be prompted to restart.

Full integration into the Tor Browser UI is likely a lot of work, so this is probably best accomplished by the agent popping up a dialog box when the update is complete (or using GNotification ~~and a system tray icon/menu~~~).

Edit: Due to time constraints this ticket primarily concerns background update checks.