Conditional header in wordpress

Question

I'm trying to have two different headers display for the homepage and for anything else. I set in wordpress settings > reading : the homepage as a "static page" a page I pubblished named "Homepage". My code should display the <div class="home_header"></divin the homepage and <div class="page_header"></div> in all other pages or posts. The code doesn't seem to work and displays <div class="page_header"></div> to all pages, Homepage included.

my code is

<header id="masthead" class="site-header">
    <div class="site-branding">
        <?php
        
        if ( is_front_page() && is_home() ) :
            ?>
            <div class="home_topbar">
                <div class="contatti_sx">
                    <address>Via Indirizzo, 2, 00000 Paese RE</address><a href="tel:+393335554444">+39 333 555 4444</a>
                </div>
                <div class="socials">
                    <a href="https://www.facebook.com"><i></i></a>
                    <a href="https://www.instagram.com"><i></i></a>
                </div>
                <div class="language">
                    <a href="">IT</a><a href="">EN</a>
                </div>
            </div>
            <div class="copertina">
                <h4>EMILIA - La Bassa</h4>
                <h1 class="site-title"><a href="<?php echo esc_url( home_url( '/' ) ); ?>" rel="home"><?php bloginfo( 'name' ); ?></a></h1>
                <img src="<?php the_post_thumbnail() ?>" alt="">
            </div>

            <div class="menu_bar">
                <div class="logo"><?php the_custom_logo(); ?></div>
                <nav id="site-navigation" class="main-navigation">
                    <button class="menu-toggle" aria-controls="primary-menu" aria-expanded="false"><?php esc_html_e( 'Primary Menu', 'cdnonni' ); ?></button>
                    <?php
                    wp_nav_menu(
                        array(
                            'theme_location' => 'menu-1',
                            'menu_id'        => 'primary-menu',
                        )
                    );
                    ?>
                </nav><!-- #site-navigation -->
                <div><a href="prenotazioni" class="prenotazioni"></a></div>
            </div>
            <?php
        else :
            ?>
            <div class="page_topbar">
                <div class="contatti_sx">
                    <address>Via Indirizzo, 2, 00000 Paese RE</address><a href="tel:+393335554444">+39 333 555 4444</a>
                </div>
                <h1 class="topbar_title"><a href="<?php echo esc_url( home_url( '/' ) ); ?>" rel="home"><?php bloginfo( 'name' ); ?></a></h1>
                <div class="socials">
                    <a href="https://www.facebook.com"><i></i></a>
                    <a href="https://www.instagram.com"><i></i></a>
                </div>
                <div class="language">
                    <a href="">IT</a><a href="">EN</a>
                </div>
            </div>
            <div class="menu_bar">
                <div class="logo"><?php the_custom_logo(); ?></div>
                <nav id="site-navigation" class="main-navigation">
                    <button class="menu-toggle" aria-controls="primary-menu" aria-expanded="false"><?php esc_html_e( 'Primary Menu', 'cdnonni' ); ?></button>
                    <?php
                    wp_nav_menu(
                        array(
                            'theme_location' => 'menu-1',
                            'menu_id'        => 'primary-menu',
                        )
                    );
                    ?>
                </nav><!-- #site-navigation -->
                <div><a href="prenotazioni" class="prenotazioni"></a></div>
            </div>
            
            <?php
        endif;
      ?>
    </div><!-- .site-branding -->

    
</header><!-- #masthead -->

which can be summarized to

<header id="masthead" class="site-header">
    <div class="site-branding">
        <?php
        
        if ( is_front_page() && is_home() ) :
            ?>
            <div class="home_header">
            </div>

            <?php
        else :
            ?>

            <div class="page_header">
            </div>
            
            <?php
        endif;
      ?>
    </div><!-- .site-branding -->

    
</header><!-- #masthead -->

where did I make a mistake? Thank you!