I think the problem is that moving from Lambda/FaaS to a container-centric alternative (ECS and friends) requires a complete re-architect of your stack. Not really. I converted a Node/Express API running in lambda using the proxy integration to a Docker/Fargate implementation in less than a couple of hours by following a Fargate tutorial. Most of that time was spent learning enough Docker to do it.
The only difference between the Docker implementation of the API and the lambda implementation was calling a different startup module.
There is nothing magical about any lambda, from the programming standpoint you just add one function that accepts a JSON request and a lambda context.
Converting it to a standalone service (outside of APIs) is usual a matter of wrapping your lambda in something that runs all of the time and routing whatever event you’re using to trigger to a queue.