With a full engine, the parent application inherits the routes from the engine. It is not necessary to specify anything in parent_app/config/routes.rb. Specifying the gem in Gemfile is enough for the parent app to inherit the models, routes etc. The engine routes are specified as:

# new_engine/config/routes.rb 
Rails.application.routes.draw do 
  # whatever 
end

No namespacing of models, controllers, etc. These are immediately accessible to the parent application.

I added routes directory to application config directory and added it in autoload_paths to ensure that routes are reloaded when these files change.

# config/application.rb
config.autoload_paths << Rails.root.join('config/routes')

Then moved necessary routes to small files like this.