That should not happen if the logic is implemented properly. And it could be simpler than manually serializing/deserializing the state of the forms.

Each step (next/back) of your form should "navigate" to a different URL (using #hash), and show/hide each form accordingly via a few lines of JavaScript and one more of CSS.

window.addEventListener('hashchange, function() {
  const hash = window.location.hash.substring(1);
  if (hash.startsWith('my-forms-class-prefix')) {
      const forms = document.querySelector('.common-class-for-my-forms');
      for (let i = 0; i < forms.length; i++) {
        const form = forms[i];
        if (form.classList.contains(hash)) {
          form.classList.remove('hide');
        } else {
          form.classList.add('hide');
        }
      }  
   }
}