You might be running into a recent issue with Azure.Identity (it is not really an issue with Azure.Identity, rather one of it's dependencies, but still). The short-term fix is pinching the cryptography module in your requirements.txt to version 43.0.3.
https://github.com/Azure/azure-sdk-for-python/issues/38725

To confirm that you are having this issue, you can check in Azure Functions - Diagnose and Solve Problems - search for "triggering" - there should be a page for "Functions that are not triggering", there should be an error there pointing you in this direction.