Or, you use a broker like Vault to which you authenticate with that JWT, and which generates a just in time ephemeral username/password for your database, which gets rotated at some point.
It's not quite a zero-trust solution though due to the CA chain of trust.
mTLS is security at a different layer though than IP source whitelisting. I'd say that a lot of companies we spoke to would want both as a defense-in-depth measure. Even with mTLS, network whitelisting is relevant. If your certificate were to be exposed for instance, an attacker would still need to be able to forge a source IP address to start a connection.
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....