How can I duplicate the add to cart button on the single product page, but redirect to another page?

Solution:

I have divided my answer into 3 parts. The intention is to add a copy of the existing add to cart button with 1 difference, and we will use that difference for the redirect.

Step 1) Adding the (copy) of the add to cart button can be done by adjusting/overwriting the template file, however it can also be done by using the available hooks in the template file, for example the woocommerce_after_add_to_cart_button hook

// Add new/extra button
function action_woocommerce_after_add_to_cart_button() {
    global $product;
    
    // Button text
    $button_text = __( 'My new text', 'woocommerce' );
    
    // Is a WC product
    if ( is_a( $product, 'WC_Product' ) ) {
        // Simple products
        if ( $product->is_type( 'simple' ) ) {
            echo '<button type="submit" name="add-to-cart" value="'. esc_attr( $product->get_id() ) . '" class="single_add_to_cart_button button alt custom_redirect_button">' . $button_text . '</button>';
        // Variable products
        } elseif( $product->is_type( 'variable' ) ) {
            echo '<button type="submit" class="single_add_to_cart_button button alt custom_redirect_button">' . $button_text . '</button>';
        }
    }
}
add_action( 'woocommerce_after_add_to_cart_button', 'action_woocommerce_after_add_to_cart_button', 10 );

This adds a copy of the existing add to cart button for simple and variable products but with 1 difference. Namely: when the button is clicked, a hidden input field is added via jQuery (step 2).

Step 2) This is the code to add the hidden input field with a certain value. I added the jQuery via an action hook but this can just as well be included in an external js file.

// Add jQuery to footer
function action_wp_footer() {
    // Only on single product page
    if ( is_product() ) {
        ?>
        <script type="text/javascript">
        jQuery( function($) {           
            // Add to cart button or custom button is clicked
            $( document ).on( 'click', '.custom_redirect_button', function () {
                // NOT disabled
                if ( ! $( this ).hasClass( 'disabled' ) ) { 
                    // Add hidden input field after
                    $( this ).after( '<input type="hidden" name="custom-redirect" value="my-value" />' );
                }
            });
        });
        </script>
        <?php
    }
}
add_action( 'wp_footer', 'action_wp_footer', 10 );

Step 3) Get the value from the hidden input field and when it matches, then it is our custom button and we apply our own url.

// Redirect
function filter_woocommerce_add_to_cart_redirect( $redirect_url, $product ) {   
    // If value isset
    if ( isset( $_REQUEST['custom-redirect'] ) ) {      
        // If equal to
        if ( $_REQUEST['custom-redirect'] == 'my-value' ) { 
            // URL to redirect to (1 is the page ID here)
            $redirect_url = get_permalink( 1 );
        }
    }

    return $redirect_url;
}
add_filter( 'woocommerce_add_to_cart_redirect', 'filter_woocommerce_add_to_cart_redirect', 10, 2 );