wp_nav_menu – page template name as item class

Is there any way to display template name (or page-template.php filename) in each menu items’ class?
Maybe using wp_nav_menu walker?

Specifically, I’m using standard menu call:

wp_nav_menu( array( 'menu' => 3, 'container' => false )

Which gives me:

<div class="menu-wrap">
<ul id="menu-menu" class="menu">
<li id="menu-item-979" class="menu-item menu-item-type-post_type menu-item-object-page menu-item-979"><a href="#">Homepage</a></li>
<li id="menu-item-844" class="menu-item menu-item-type-post_type menu-item-object-page menu-item-844"><a href="#">Subpage</a></li>
</ul>
</div>

And if I have template names Homepage and Subpage, I’d like to get the same, but with template name classes:

<div class="menu-wrap">
<ul id="menu-menu" class="menu">
<li id="menu-item-979" class="menu-item menu-item-type-post_type menu-item-object-page menu-item-979 Homepage"><a href="#">Homepage</a></li>
<li id="menu-item-844" class="menu-item menu-item-type-post_type menu-item-object-page menu-item-844 Subpage"><a href="#">Subpage</a></li>
</ul>
</div>

Thanks!

The nav_menu_css_class filter will let you add CSS classes to specific menu items. We combine that with the get_page_template_slug function to fetch the page template filename, then we use that with the get_page_templates method of the theme class to get the template name as defined in the Template Name: header. Then we pass that result through sanitize_html_class to make it a valid class name. Lastly, we add it to the array of classes and return it.

function wpd_page_template_nav_class( $classes, $item ) {
    // only check pages
    if( 'page' == $item->object ){
        // if this page has a template assigned
        if( $slug = get_page_template_slug( $item->object_id ) ){
            // get the array of filenames => template names in the current theme
            $templates = wp_get_theme()->get_page_templates();
            // if there is a template with key matching our filename
            if( isset( $templates[$slug] ) ){
                // sanitize it and add it to the classes
                $classes[] = sanitize_html_class( $templates[$slug] );
            }
        }
    }
    return $classes;
}
add_filter( 'nav_menu_css_class', 'wpd_page_template_nav_class', 10, 2 );