Add dropdown list on WooCommerce checkout page when coupon is applied

You can use a checkout JS event in the WooCommerce frontend, in this case

$( document.body ).trigger( 'applied_coupon_in_checkout' );
$( document.body ).trigger( 'removed_coupon_in_checkout' );

So you get:

function action_woocommerce_review_order_before_payment() {
    $content = '<div id="store-pickup-select">';
    $content .= '<select>';
    $content .= '<option selected="selected">Choose one</option>';
    $content .= '<option value="my-option">My option</option>';
    $content .= '</select>';
    $content .= '</div>';
    
    echo $content;
}
add_action( 'woocommerce_review_order_before_payment', 'action_woocommerce_review_order_before_payment', 10, 0 );

// jQuery code
function action_wp_footer() {
    if ( is_checkout() && ! is_wc_endpoint_url() ) {
    ?>
    <script type="text/javascript">
    jQuery(function($) {
        // Default
        $( '#store-pickup-select' ).hide();
        
        $( document.body ).on( 'applied_coupon_in_checkout removed_coupon_in_checkout', function( event ) {
            // With no parameters, the .toggle() method simply toggles the visibility of elements:
            $( '#store-pickup-select' ).toggle();
        });
    });
    </script>
    <?php
    }
}
add_action( 'wp_footer', 'action_wp_footer' );