How to get correct URLs in network wide menu (Multisite)?

You just need the last part of your function where you switch to blog 1 and get the menu.

function wp_multisite_nav_menu() {
    
    $args = [
        'menu' => 'Main Menu',
        'theme_location' => 'main-nav'
    ];

    switch_to_blog( 1 );

    echo wp_nav_menu( $args );

    restore_current_blog();
}