You can try this code
For listing details page override this plugin file plugins/classified-listing/templates/listing/actions.php using child theme.
copy the file and paste it in following location child-theme/classified-listing/listing/actions.php then add this condition in line no 22 is_user_logged_in()
line 22 to 24 full code –
<?php if ($can_add_favourites && is_user_logged_in()): ?>
<li class="list-group-item" id="rtcl-favourites"><?php echo Functions::get_favourites_link($listing_id); ?></li>
<?php endif; ?>
For the listing archive page, add below code in child theme functions.php file
remove_action('rtcl_listing_meta_buttons', [\Rtcl\Controllers\Hooks\TemplateHooks::class, 'add_favourite_button'], 10);
add_action('rtcl_listing_meta_buttons', function() {
global $listing;
if (\Rtcl\Helpers\Functions::is_enable_favourite() && is_user_logged_in()) { ?>
<div class="rtcl-btn"
data-tooltip="<?php esc_html_e("Add to favourite", "classified-listing") ?>"
data-listing_id="<?php echo absint($listing->get_id()) ?>">
<?php echo \Rtcl\Helpers\Functions::get_favourites_link($listing->get_id()) ?>
</div>
<?php }
}, 10);
Thanks