kifisearch.module

<?php

use Drupal\Core\Form\FormStateInterface;

function kifisearch_form_search_form_alter(array &$form, FormStateInterface $form_state, $form_id) {
  // In order to provide theme suggestions, we need to add the search page ID to theme.
  if ($form_id == 'search_form') {
    $form['#theme'] = ['search_form__' . $form_state->get('search_page_id')];

    // Also set the search page ID somewhere so that we can identify forms in other hooks.
    $form['#search_id'] = $form_state->get('search_page_id');
  }
}

function kifisearch_theme_suggestions_form_alter(array &$suggestions, array $variables) {
  // Provide theme suggestions as the core module does not do this by itself.

  $form_id = $variables['element']['#form_id'] ?? null;

  if ($form_id == 'search_form') {
    $theme = reset($variables['element']['#theme']);
    $parts = explode('__', $theme);

    foreach ($parts as $i => $part) {
      $suggestions[] = implode('__', array_slice($parts, 0, $i + 1));
    }
  }
}