feat(core): use experimental route handlers instead of api routes

[plushdohn]

I don't like that Catalyst still depends on Next's pages directory for its back-end. We should fully embrace the new app directory and use route handlers instead.

The new folder structure when using Catalyst might become:

app/
 catalyst/
  [[...catalyst]]/
   page.ts // Root page
  api/
   [...catalyst]/
    route.ts // Root endpoint

This might not be completely straight-forward as route handlers need a named export for each HTTP method, so the API might get a little dirtier. We also need to keep working around Auth.js requirements for auth endpoints.