Ciao, prova in questo modo:
codice:
let display;
let edit;

let initialContents =  "<style> \n.intro { \ncolor: yellow; \ntext-decoration: underline; \ntext-align: center;\n} \n</style>\n\n<h3 class='intro'>Designed by Dillion Megida</h3>";
  
display = document.getElementById('display');
edit = document.getElementById('edit');

edit.innerText = initialContents;
display.innerHTML = initialContents;

window.addEventListener('keyup', () => {
  edit = document.getElementById('edit');
  editContainer = edit.innerText;
  display = document.getElementById('display');
  display.innerHTML = editContainer;
});
Ho eliminato le parti che riguardano il localStorage.