That said, I agree with you about the other generalisations!

EDIT: actually, where do PaaSes fit into this taxomony? I'd argue that level 2 is actually the PaaS level. You might choose an edge PaaS (Workers), distributed (Fly.io), or centralised (Elastic Beanstalk) depending on your needs. But ultimately this level is: "I write code, you run it". FaaSes are a subset of PaaS providers which focus on stateless models, but there's no reason you can't combine FaaS for your code with a managed database offering.