Computer Configuration > Administrative Templates > Microsoft Edge > Default search provider
Both
HKLM\Software\Policies\Microsoft\Edge
Specifies the keyword, which is the shortcut used in the Address Bar to trigger the search for this provider. This policy is optional. If you don't configure it, no keyword activates the search provider. This policy is applied only if you enable the 'DefaultSearchProviderEnabled' (Enable the default search provider) and 'DefaultSearchProviderSearchURL' (Default search provider search URL) policies. Starting in Microsoft Edge 84, you can set this policy as a recommended policy. If the user has already set a default search provider, the default search provider configured by this recommended policy will not be added to the list of search providers the user can choose from. If this is the desired behavior, use the 'ManagedSearchEngines' (Manage Search Engines) policy. Example value: mis