If you want to stay on the Kubernetes route check out k3s. Super easy to setup and usable for small production workloads
I always thought that one of the advantages of going serverless was that you didn't have to worry about keeping the underlying operating system up-to-date. No needing to do a monthly "sudo apt update && apt upgrade" or whatever. But containers throw that all away when container images enter the world.
Instead of updating your operating system, you're updating your images...and it's basically the same thing.
Most would say even a server-ful system (k8s, or whatever) should be considered 'cattle not pets' with immutable nodes replaced as needed anyway. No update, just replace. Just like building a new image and having new pods (or serverless whatevers) pull it.
If you're truly "serverless" by my interpretation of it, then you wouldn't care. Your cloud provider will have updated their infrastructure, and that's all that matters.
In fact almost nothing is serverless (well, the truth comes out! ;)) by that definition, since even Lambda has runtime versions to choose/upgrade, Managed-Acme has Acme versions, etc.
SES, SNS, SQS, etc. sure, but I suppose no compute, since you need libraries, and libraries have versions, and you can't have them (significantly/major versions) changing under your feet. (Or if they don't have versions they're of course destined to have known security holes.)
(Or it's not even about libraries if you want to say no you don't need libraries - it's just about having to interface with anything.)
I’ve never cordoned off an individual head of cattle and lobotomized it, which is kinda what we do when debugging issues. We take the pod out of rotation, flip a bunch of configs, then give it some traffic to see the new debugging statements.