At Slite, for all outgoing calls we use a sandboxed proxy. It has saved us a few times already. We detailed the trick in a blog post -> https://slite-tech-blog.ghost.io/anti-ssrf-solution/

This is the path I've seen be fairly robust at a few tech companies I've helped sort out this defense for. I've helped write libraries too but the proxy is the easiest approach when targeting many languages.

For half of those it's called a firewall and for the other half you should specify timeouts / max redirects.

Outgoing webhooks dispatched from a Lambda seemed to solve most of the above problems for us

Using lambda doesn't protect you against any of these.

Timeout attacks: instead of failing you'll now be just be paying through the nose. And also with enough scale you can hit lambda limits and fail.

SSRF: you are still as vulnerable unless the lambda is outside your VPC (but then it's the VPC that solved it, not the lambda).