Hey, @papermelon
The LoginPress login form appears only on WordPress default login page i.e: /wp-login.php and I can see that your design is being displayed at wp-login.php and at the same time you have installed the WooCommerce on your website and their login and register forms are being displayed on the my-account page that is a custom login page.
You can redirect the users from my-account to WordPress default login page if users are not logged in, and once they are logged in you can redirect them back to my account page. In this way, your my-account login forms will be replaced with the LoginPress form.
Please follow the doc to learn how you can do the whole process: https://loginpress.pro/doc/loginpress-woocommerce-compatibility/
If you still face any issue you can reach us at WPBrigade
Thank you.