Burger Menu

to get a “footer-page” with dynamically feed menues – you can use the menu shortcode :

function custom_named_menu_shortcode( $atts ) {
    extract( shortcode_atts( array(
        'name'  => '', // Default to an empty menu name
        'class' => 'custom-menu', // Default CSS class
        'depth' => 0, // Default depth (0 for unlimited)
        'title' => '', // New: Default to an empty title
        'title_tag' => 'h2', // New: Default title HTML tag
        'title_class' => 'menu-title', // New: Default title CSS class
    ), $atts ) );

    $output = ''; // Initialize output variable

    // If a title is provided, add it to the output
    if ( ! empty( $title ) ) {
        $output .= '<' . esc_attr( $title_tag ) . ' class="' . esc_attr( $title_class ) . '">' . esc_html( $title ) . '</' . esc_attr( $title_tag ) . '>';
    }

    if ( ! empty( $name ) ) {
        $output .= wp_nav_menu( array(
            'menu'            => $name,
            'menu_class'      => $class,
            'container'       => 'nav', // You can change this to 'div', false, etc.
            'container_class' => $class . '-container',
            'echo'            => false, // Important: returns the menu HTML instead of printing it
            'depth'           => $depth,
        ) );
    }
    return $output; // Return the accumulated output
}
add_shortcode( 'named_menu', 'custom_named_menu_shortcode' );

it is used like this:
[named_menu name="your-menu-name" class="my-custom-menu" depth="2" title="Our Main Menu"]

then you can setup your layout with codeblock elements – each of them represents a menu ( or different shortcode – f.e. social-media )

but for that i wouldn’t use the enfold burger icon – instead i would place a custom Button – perhaps a fixed button to toggle a class to hide/show this page.

see here example with “burger” always visible – and with #footer-page as overlay.

https://basis.webers-testseite.de/

if you are interested in that – i gave you a step by step guide.