Yes. You can add any id and class to a form by adding the html_id and html_class attributes into a [contact-form-7] shortcode.
[contact-form-7 id="1234" title="Contact form 1" html_id="contact-form-1234" html_class="form contact-form"]
<?php previous_post_link('%link', '<img src="'. get_stylesheet_directory_uri() . '/assets/images/list-arrow.svg" alt="Icon">'.sprintf(get_theme_mod('btn_text_prev', 'Предедущая новость')).'', true); ?>
<?php
/* ваш код обновления post_title */
/* ... */
$post->post_name = sanitize_title($post->post_title);
/* ... */
/* ваш код сохранения */
БЕЗ ПЛАГИНА.