Computer Configuration > Administrative Templates > Microsoft Edge
Both
HKLM\Software\Policies\Microsoft\Edge
A search box is an additional text input field located next to the address bar in a web browser. It allows users to perform web searches directly from the browser interface. If you enable or don't configure this policy, the search box will be visible and available for use. Users can toggle the search box in Edge Settings page edge://settings/appearance#SearchBoxInToolbar. If you disable this policy, search box will not be visible, and users will have to use the address bar or navigate to a search engine to perform web searches.