You are correct in that the calling out to other things is just a concern of the function itself, but the value in the 'connecting' that Lambda does is from being _invoked_ by other Cloud services by way of integration to their event systems. e.g. Object storage file creation event X triggers Lambda function Y to update resource Z (resource Z isn't necessarily a Cloud service, it could be a database).
This is why I'm skeptical of on-prem FaaS. It's an easy value proposition to sell when you can use Lambda as an example. But Enterprises have heterogeneous environments so Lambda-like integration into other services is far from a given, and 'scaling to zero' is a little disingenuous because there always needs to be underlying infrastructure (k8s in the case of PFS) running to handle function invocation.