Hi Robert,
As far as I know, Big Maps is the only one the has functionality to calculate a route by transit:
Bing Maps Routes API
https://learn.microsoft.com/en-us/bingmaps/rest-services/routes/
I do not believe Azure Maps has the capability to do so:
Azure Maps Mobility Services Preview will be retired on 5 October 2021
https://azure.microsoft.com/en-us/updates/azure-maps-mobility-services-preview-retirement/
If this is helpful please accept answer.