Great question — answering as the UphillTech team:
To change the URL of continue shopping button, you need to do some changes in the theme code. In the theme code editor, find the file named: main-cart-items.liquid and search for search for cart__empty-text Screen shot for reference Now you need to change the href of a tag to {{ routes.root_url }} Screen shot for reference
Full answer by Christine Shpeherd: https://stackoverflow.stackexchange.com/a/78758772 (CC BY-SA 4.0).
Want it for your business? UphillTech.