Computer Configuration > Administrative Templates > Microsoft Edge - Default Settings (users can override)
Both
HKLM\Software\Policies\Microsoft\Edge\Recommended
Allows Microsoft Edge processes to start at OS sign-in and keep running after the last browser window is closed. In this scenario, background apps and the current browsing session remain active, including any session cookies. An open background process displays an icon in the system tray and can always be closed from there. If you enable this policy, background mode is turned on. If you disable this policy, background mode is turned off. If you don't configure this policy, background mode is initially turned off, and the user can configure its behavior in edge://settings/system.