Add reproduction

app/router.js

@@ -6,4 +6,6 @@ export default class Router extends EmberRouter {
   rootURL = config.rootURL;
 }
 
-Router.map(function () {});
+Router.map(function () {
+  this.mount('foo');
+});

app/templates/application.hbs

@@ -1,7 +1,5 @@
-{{page-title "Example"}}
+<h1>Host app</h1>
 
-{{!-- The following component displays Ember's default welcome message. --}}
-<WelcomePage />
-{{!-- Feel free to remove this! --}}
+<LinkTo @route='foo'>Go to Foo Engine</LinkTo>
 
 {{outlet}}

lib/foo/addon/controllers/application.js

@@ -0,0 +1,17 @@
+import Controller from '@ember/controller';
+import { action } from '@ember/object';
+import { inject } from '@ember/service';
+import { tracked } from '@glimmer/tracking';
+
+export default class ApplicationController extends Controller {
+  queryParams = ['page'];
+
+  @tracked page = 1;
+
+  @inject router;
+
+  @action
+  goToPage1() {
+    this.router.transitionTo({ queryParams: { page: 1 } });
+  }
+}

lib/foo/addon/engine.js

@@ -0,0 +1,15 @@
+import Engine from 'ember-engines/engine';
+import loadInitializers from 'ember-load-initializers';
+import Resolver from './resolver';
+import config from './config/environment';
+
+const { modulePrefix } = config;
+
+const Eng = Engine.extend({
+  modulePrefix,
+  Resolver,
+});
+
+loadInitializers(Eng, modulePrefix);
+
+export default Eng;

lib/foo/addon/resolver.js

@@ -0,0 +1,3 @@
+import Resolver from 'ember-resolver';
+
+export default Resolver;

lib/foo/addon/routes.js

@@ -0,0 +1,5 @@
+import buildRoutes from 'ember-engines/routes';
+
+export default buildRoutes(function () {
+  // Define your engine's route map here
+});

lib/foo/addon/templates/application.hbs

@@ -0,0 +1,14 @@
+<h2>Foo Engine</h2>
+
+Click me first:
+
+<LinkTo @route='application' @query={{hash page=2}}>Go to page 2</LinkTo>
+
+<br />
+<br />
+
+Then click me:
+
+<button type='button' {{on 'click' this.goToPage1}}>Go to Page 1</button>
+
+{{outlet}}

lib/foo/config/environment.js

@@ -0,0 +1,11 @@
+/* eslint-env node */
+'use strict';
+
+module.exports = function (environment) {
+  let ENV = {
+    modulePrefix: 'foo',
+    environment,
+  };
+
+  return ENV;
+};

lib/foo/index.js

@@ -0,0 +1,16 @@
+/* eslint-env node */
+'use strict';
+
+const EngineAddon = require('ember-engines/lib/engine-addon');
+
+module.exports = EngineAddon.extend({
+  name: 'foo',
+
+  lazyLoading: Object.freeze({
+    enabled: false,
+  }),
+
+  isDevelopingAddon() {
+    return true;
+  },
+});

lib/foo/package.json

@@ -0,0 +1,11 @@
+{
+  "name": "foo",
+  "keywords": [
+    "ember-addon",
+    "ember-engine"
+  ],
+  "dependencies": {
+    "ember-cli-htmlbars": "*",
+    "ember-cli-babel": "*"
+  }
+}