Hi!
In the setting for a Web Map you can "Enable Search" and check "By layer" to add map specific search support based on the layers. Even if you uncheck "By adress" the default search in the map includes Esri World Geocoder, is set to "All" and the placeholder text is "Find adress or place". This is not true for Field Maps.
I want to be able to further customize search functionality, and totally remove "Esri World Geocoder" from the search results in a Web Map. This is possible if you integrate the map in an Experience Builder, remove the search tool from the map and replace it with a Search widget. The customization you make should also be reflected in a Dashboard based on the Web Map.