The Free Shipping Bar always gets the total order amount from Shopify. If the coupon code was applied on the cart page, the Free Shipping Bar would reflect this change.
However, it is a bit different when it comes to the checkout page. Shopify does not allow any apps to access the checkout page for security reasons. Therefore, even if a customer applies a coupon code during the checkout process, the Free Shipping Bar cannot display any message at this moment
Please note that if a customer applies a coupon code in the checkout page that causes the total value in the cart to fall below the free shipping goal, the Free Shipping Bar's message will once again display the initial message because it will take the total value into consideration, not the total before the coupon was applied.