Auth0 sell a bunch of authentication products that are similar/compete with cognito.
The difference between cognito and auth0 is that auth0 has documentation, code examples and a decent API guide.
Cognito has a poorly documented API, terrible integration guides and even worse debugging options
Once you have it going, cognito is grand. To get there, its a huge learning curve
The fact that some specific attributes or options cannot change after creation is hard too. Other than that, it's not too bad. But like you said, setting it up takes effort, but a lot of programming is getting to a non trivial hello world.
What do they mean by that?
auth0 is a company that sells a variety of authentication solutions (on premise and SaaS) and a variety of authentication libraries/plugins.
For example they run the site https://jwt.io/ that anybody who's had to work with JWT tokens would have used at some point.