Can't mount newly generated Rails engine in an app

Question

I have a complex Rails app and I want to extract some core functionality into an engine so that I can reuse the models etc in other Rails apps.

I've been following the official documentation for engines (https://guides.rubyonrails.org/engines.html). I'm able to create a new engine inside the app and generate some test models

> rails plugin new testengine --mountable

testengine> rails generate model Test

This is the .gemspec

require_relative "lib/testengine/version"

Gem::Specification.new do |spec|
  spec.name        = "testengine"
  spec.version     = Testengine::VERSION
  spec.authors     = ["Me"]
  spec.summary     = "testengine"

  # Prevent pushing this gem to RubyGems.org. To allow pushes either set the 'allowed_push_host'
  # to allow pushing to a single host or delete this section to allow pushing to any host.
  spec.metadata["allowed_push_host"] = "TODO: Set to 'http://mygemserver.com'"

  spec.files = Dir["{app,config,db,lib}/**/*", "Rakefile", "README.md"]

  spec.add_dependency "rails", "~> 6.1.4"
end

I console into the test dummy rails app in testengine, and I can find my new model at Testengine::Test, no problem. So far so good.

Now I get to section 4.1 Mounting the Engine. I add the engine via the Gemfile file (in fact this is already done for me thanks to the rails generator above).

gem 'testengine', path: 'testengine'

I console into the main app and I can find Testengine and Testengine::VERSION but not Testengine::Engine or Testengine::Test.

Reading a little further the docs say you need add this line to config/routes.rb

mount Testengine::Engine, at: "/testengine"

I do and now the rails app won't even start

config/routes.rb:3:in `block in <top (required)>': uninitialized constant Testengine::Engine (NameError)

What did I miss?