Lit reactive controllers fail to requestUpdate in nested components

I want to create a basic state management using Lit reactive controllers. The purpose is to share property values accross the application.

The issue occurs when a controller is attached to a view and to a component nested in the view. When value inside controller changes, the value in the view gets updated, but not in the nested component.

Example: state.js contains the store logic. A view access the store to create a value and show state value. Nested components also show state value.

state.js

export class StateController {

  static get properties() {
    return {
      state: { type: Object },
      host: { type: Object }
    }
  }

  constructor(host) {
    // Store a reference to the host
    this.host = host;
    this.state = {};

    // Register for lifecycle updates
    host.addController(this);
  }

  _setStoreValue(property, val) {
    this.state[property] = val;
    this.host.requestUpdate();
  }
}

component.js

import { LitElement, html } from 'lit';
import { StateController } from '../state.js';

export class TestComponent extends LitElement {

  static get properties() {
    return {
      stateCtrl: { type: Object },
      state: { type: Object },
    };
  }

  constructor() {
    super();
    this.stateCtrl = new StateController(this);
    this.state = this.stateCtrl.state
  }

  render() {
    return html` Value in component: ${this.state?.test} `;
  }
}

customElements.define('test-component', TestComponent);

view.js

import { LitElement, html } from 'lit';
import { StateController } from '../state.js';
import './test-component.js';

export class MonTodo extends LitElement {
  static get properties() {
    return {
      stateCtrl: { type: Object },
      state: { type: Object  },
    };
  }

  constructor() {
    super();
    this.stateCtrl = new StateController(this);
    this.state=this.stateCtrl.state
  }

  render() {
    return html`
      <button @click=${() => this.setValueTest()}>Set value to 3</button>
      Value in view: ${this.state?.test}
      <h3> Component 1</h3>
      <test-component></test-component>
      <h3> Component 2</h3>
      <test-component></test-component>

          `;
  }

  setValueTest() {
    this.stateCtrl._setStoreValue("test", 3)
  }
}

customElements.define('mon-todo', MonTodo);

A button click in view.js updates this.state.test in view.js but not in component.js