Site builders don't export a working website. You can usually take your text, images and, sometimes, blog posts, but the design and layout stay behind. That is fine: the new site is designed from scratch anyway. What matters is listing every page address before you cancel, so each one can redirect to its new home.
Keep the builder subscription running until the new site is live and the redirects are tested. If your domain was bought through the builder, you can transfer it or simply point it at the new site; either way it stays yours.
We don't rebuild on WordPress, Shopify or Webflow. If you want to stay on one of those, a specialist in that platform is the better choice.