Serverless means spinning compute resources up on demand in the cloud vs. running a server permanently.
Not quite. Serverless means you can run a server permanently, but you need pay someone else to manage the infrastructure for you.
That's not what serverless means at all. Most function-as-a-service offerings require developers to bother about infrastructure aspects, such as runtimes and even underlying OS.
They just don't bother about managing it. They deploy their code on their choice of infrastructure, and go on with their lives.