When adding to cart a shoe from our site on the category hover, it then takes you to the product, we would like it to stay on the page, is there a way to do this?
Try to use the Ajax add to cart and check how it works. Navigate to WooCommerce > Settings > Products > enable Ajax add to cart buttons on archive pages.
If you have another behavior, share some screenshot or example for better understanding so i will check and give you a possible solution. Also, share the valid login details of your site.
Sorry to say that your given login details are not working, please share the correct login details of your site. So I will further check on your site and give you a possible solution.
You are using the variable product in archive products. When you click on the select option you need to choose the product variation. Try to use the shopping cart widget from Theme Settings > Shop > Shopping cart widget > action after add to cart button “display widget”.
Please deactivate all the 3rd party plugins and activate only theme-required plugins on the site and then check the issue. I am sure your issue will be solved. Then Activate the 3rd party plugins one by one and check which plugin is creating the issue for you.
Otherwise, if the issue still exists then keep the 3rd party plugins deactivated and let me know I will check and give you a possible solution.