The Azure Maps reverse geocoding service does have an option to return speed limits: https://learn.microsoft.com/en-us/rest/api/maps/search/getsearchaddressreverse Set the returnSpeedLimit parameter to true.
The routing service in Azure Maps provides details on the current effective speed of traffic on the road depending on current or predicted traffic. This isn't the speed limit but instead tells you what the speed of vehicles are, or likely to be. The vector traffic flow tiles also provide the raw traffic flow information which can be used for seeing this info in bulk.