How can I ensure my custom web component updates correctly when its attributes change in different browsers?

<!-- BEGIN COPY / PASTE -->
        class MyComponent extends HTMLElement {
            static get observedAttributes() {
                return ['my-attribute'];
            }

            constructor() {
                super();
                this.attachShadow({ mode: 'open' });
                this.shadowRoot.innerHTML = `<p>Initial content</p>`;
            }

            attributeChangedCallback(name, oldValue, newValue) {
                if (name === 'my-attribute') {
                    this.shadowRoot.querySelector('p').textContent = `Attribute changed to: ${newValue}`;
                }
            }
        }

        customElements.define('my-component', MyComponent);
        <!-- END COPY / PASTE -->