The easiest way to get similar results for reverse geocoding in Azure Maps compared to Bing Maps is to use the latest Azure Maps reverse geocoding service: https://learn.microsoft.com/en-us/rest/api/maps/search/get-reverse-geocoding?view=rest-maps-2024-04-01&tabs=HTTP
Version 1 of the reverse geocoding service is purely based on TomTom, while the latest version uses the same data set as Bing Maps and should provide nearly identical results (with a new response format).