I'm not entirely what you mean with “default map provider” but depending on what you need this may work for you: https://kagi.com/settings?p=redirects

Edit: Ah I suppose that you meant the “Inline Maps”. Unfortunately there doesn't seem to be a way to change the provider, only to enable/disable the feature: https://kagi.com/settings?p=more_search

When I search for a city, along with the list of results, there is a map on the right. When I click on it, it doesn't go to Google Maps.

Very likely due to the cost of the maps api.