Computer Configuration > Administrative Templates > Microsoft Edge
Both
HKLM\Software\Policies\Microsoft\Edge
Allows the Search bar to start running at Windows startup. If you enable: The Search bar will start running at Windows startup by default. If the Search bar is disabled via 'SearchbarAllowed' (Enable the Search bar) policy, this policy will not start the Search bar on Windows startup. If you disable this policy: The Search bar will not start at Windows startup for all profiles. The option to start the search bar at Windows startup will be disabled and toggled off in search bar settings. If you don't configure the policy: The Search bar will not start at Windows startup for all profiles. The option to start the search bar at Windows startup will be toggled off in search bar settings.