https://learn.microsoft.com/en-us/azure/cosmos-db/nosql/sdk-connection-modes#service-port-ranges talks about which ports need to be open for Azure Cosmos DB to work properly.
I have an app service which queries Azure Cosmos DB.
How can I check which ports are open on the app service?
Afaik all outbound ports are open. So no problem there. Inbound ports are a different story, that's only 80 and 443. But to connect to CosmosDb (outbound) you don't have to do anything.