Add the Form name to the theme suggestions input field
In your yourTheme.theme, you could do:

function yourTheme_form_alter(&amp;$form, \Drupal\Core\Form\FormStateInterface $form_state, $form_id) {

  foreach (\Drupal\Core\Render\Element::children($form) as $key) {
    $form[$key]['#attributes']['data-twig-suggestion'] = $form['#id'];
  }

  $form['actions']['submit']['#attributes']['data-twig-suggestion'] = $form['#id'];
}


The function \Drupal\Core\Render\Element::children($form) returns an array of all the children elements (for a form) for which the keys don't start with #.

So, this array will have the field names as its elements. Then, you iterate over the array and add the attribute data-twig-suggestion and its corresponding value. Note that the array will have some extra elements that aren't form fields, and those would also get the new attribute and its value. I don't think there is any collateral damage on that.

For the submit button ($form['actions']['submit']) we are adding the attribute "manually", as the field element (submit) is "nested" inside the actions array, so our previous loop won't have added the attribute to the correct element in the array.

Then, you also add this function:

function yourTheme_theme_suggestions_input_alter(&amp;$suggestions, array $variables) {
  $element = $variables['element'];
  if (isset($element['#attributes']['data-twig-suggestion'])) {
    $suggestion_suffix = str_replace(['-'], '_', $element['#attributes']['data-twig-suggestion']);
    $suggestions[] = 'input__' . $element['#type'] . '__' . $suggestion_suffix;
  }
}


Here, each form input field is processed and a template suggestion is added based on the previously created attribute.

PS: this solution is based on this article: Getting granular with Drupal 8 forms.