If mTLS is combined with outbound connections, then IP source whitelisting is irrelevant; the external network cannot connect to your resources.

This (and more) is exactly what we (I work on it) built with open source OpenZiti, a zero trust networking platform. Bonus points, it includes SDKs so you can embed ZTN into the serverless function, a colleague demonstrated it with a Python workload on AWS - https://blog.openziti.io/my-intern-assignment-call-a-dark-we....