Hello and welcome!
The Official Phoenix Guides is really the best resource. Elixir’s documentation is pretty fantastic and, if you’re not used to that coming from other ecosystems, I would always look there first. Controllers are absolutely still usable and will not be deprecated (websockets can’t set session data so they are at least necessary for that kind of thing). The Contexts section goes in depth about building an end-to-end feature and it uses controllers.
As for building a large SAAP app I can’t speak from experience there. Phoenix should be quite capable of building very large applications, though coming from me that is merely speculative based on others’ reports of their experience 
Here is a somewhat verbose description of hexdocs I gave to someone else who asked a similar question recently (because I didn’t notice these things right away, ha).
