If it's ephemeral to a function, it's not "storage". It's just core memory that may or may not be backed by physical "storage" media, and is organized as a tmpfs for the user's convenience.
I was working for a programmatic advertising demand side platform. We had customers that submitted all sorts of ads to us and the lambda was in charge of rendering the ad and performing some validations on it. We accomplished it in the end using layers. It was in 2017, but it feels like a lifetime ago.
What's the use case? I see a sibling commenter mentioned puppeteer which I'm aware is essentially Chrome. Are you too referring to running puppeteer in Lambda? If so, what is the purpose?
In one lambda I can load chrome, visit a website, take a screenshot and save it to S3 in around 2s with around 280mb memory used. You could keep chrome open and reuse it if available, but you can't count on it with lambda being stateless.
/tmp is ephemeral in the sense that it dies with the Lambda instance, but it is also persistent between multiple serial invocations landing on that instance, even if the instance is frozen and thawed between some of those invocations.
The process memory state on the instance (set up during the Init phase) is also available between invocations.
This is also useful for deploying a big static website with AWS CDK which currently uses a Lambda and had the limit of 512mb (it was already possible to pass it by using an attached storage but this makes it easier).