Updated controller

components.alpha-page\.js

import Component from '@glimmer/component';
import { tracked } from '@glimmer/tracking';
import { action } from '@ember/object';

export default class extends Component {
  @tracked random = this.getRandom();

  constructor() {
    super(...arguments);
    console.log('INIT: Alpha Page Component');
  }
  
  getRandom() {
    return Math.floor(Math.random() * 100)
  }
  
	@action
  regenerateRandom() {
    this.random = this.getRandom();
  }
}

components.beta-page\.js

import Component from '@glimmer/component';

export default class extends Component {
}

controllers.alpha\.js

import Controller from '@ember/controller';
import { action } from '@ember/object';

export default Controller.extend({
  init() {
    this._super(...arguments);
    console.log('INIT: Alpha Controller');
    this.set('random', this.getRandom());
  },
  
  getRandom() {
    return Math.floor(Math.random() * 100)
  },
  
  regenerateRandom: action(function() {
    this.set('random', this.getRandom());
  })
});

controllers.beta\.js

import Controller from '@ember/controller';
import { action } from '@ember/object';

export default Controller.extend({
  queryParams: ['number'],
  number: null,
  init() {
    this._super(...arguments);
    console.log('INIT: Beta Controller');
  },
  
  updateNumber: action(function(value) {
    this.set('number', value);
  })
});

controllers.gamma\.js

import Controller from '@ember/controller';

export default Controller.extend({
  init() {
    this._super(...arguments);
    console.log('INIT: Gamma Controller');
  }
});

helpers.eq\.js

import { helper } from '@ember/component/helper';

export default helper(function eq({a, b}) {
  return a === b;
});

router\.js

import EmberRouter from '@ember/routing/router';
import config from './config/environment';

const Router = EmberRouter.extend({
  location: 'none',
  rootURL: config.rootURL
});

Router.map(function() {
  this.route('alpha');
  this.route('beta');
  this.route('gamma');
});

export default Router;

routes.alpha\.js

import Route from '@ember/routing/route';

export default Route.extend({
  model() {
    return { foo: 'foo' };
  }
});

routes.beta\.js

import Route from '@ember/routing/route';

export default Route.extend({
  model() {
    return { bar: 'bar' };
  }
});

routes.gamma\.js

import Route from '@ember/routing/route';

export default Route.extend({
  model() {
    return { baz: 'baz' };
  }
});

templates.alpha\.hbs

{{!--

* Keep controllers "skinny", i.e. no logic, or don't use them at all
* Refactor to just contain components
* Much easier to test

--}}

<AlphaPage
  @model={{this.model}}
/>

templates.application\.hbs

<menu>
  <ul>
    <li>
      <LinkTo @route="index">Home</LinkTo>
    </li>
    <li>
      <LinkTo @route="alpha">Alpha</LinkTo>
    </li>
    <li>
      <LinkTo @route="beta">Beta</LinkTo>
    </li>
    <li>
      <LinkTo @route="gamma">Gamma</LinkTo>
    </li>
  </ul>
</menu>
{{outlet}}
<br>
<br>

templates.beta\.hbs

{{!--
  Query Params: the only thing controllers are good for

	* Keep controllers "skinny", i.e. no logic, or don't use them at all
	* Refactor to just contain components
	* Data down, actions up
  * Pass down actions to modify controller state

--}}

<BetaPage
  @model={{this.model}}
  @updateNumber={{this.updateNumber}}
/>

templates.components.alpha-page\.hbs

<h2>Alpha</h2>

Model: {{@model.foo}}
<br>

Random: {{this.random}}
<br>
<br>
<label>
  <button {{on "click" this.regenerateRandom}}>
  	Regenerate random
  </button>
</label>

templates.components.beta-page\.hbs

<h2>Beta</h2>

Model: {{@model.bar}}

<p>Set a number:</p>

<div>
  <input
  	type="radio"
    id="one"
    name="number"
    value="one"
    {{on "click" (fn @updateNumber "one")}}
  >
  <label for="one">One</label>
</div>

<div>
  <input
  	type="radio"
    id="two"
    name="number"
    value="two"
    {{on "click" (fn @updateNumber "two")}}
  >
  <label for="two">Two</label>
</div>

<div>
  <input
  	type="radio"
    id="three"
    name="number"
    value="three"
    {{on "click" (fn @updateNumber "three")}}
  >
  <label for="three">Three</label>
</div>

templates.gamma\.hbs

<h2>Gamma</h2>

Model: {{this.model.baz}}

templates.index\.hbs

<h2>Home</h2>

twiddle\.json

{
  "version": "0.17.1",
  "EmberENV": {
    "FEATURES": {},
    "_TEMPLATE_ONLY_GLIMMER_COMPONENTS": false,
    "_APPLICATION_TEMPLATE_WRAPPER": true,
    "_JQUERY_INTEGRATION": true
  },
  "options": {
    "use_pods": false,
    "enable-testing": false
  },
  "dependencies": {
    "jquery": "https://cdnjs.cloudflare.com/ajax/libs/jquery/3.5.1/jquery.js",
    "ember": "3.18.1",
    "ember-template-compiler": "3.18.1",
    "ember-testing": "3.18.1"
  },
  "addons": {
    "@glimmer/component": "1.0.0"
  }
}