Azure Cosmos DB doesn't support basic sort
Mongo supports case insensitive sort through collation usage.
When I tested on mongo locally it worked, when deployed on azure platform it just started throwing error:
"MongoError: server bmcldocdb.documents.azure.com:10255 does not support collation"
This work is currently under way for case insensitive sort. Collation is on long term road map.
Will update here as this moves towards general availability.
Thank you for your suggestion and votes.
Following up to see the status of collation for the Mongo API
+1 was told by Microsoft Support to post feature request here