I would like to show the configurable product options in a popup in the mobile version of my store
Use the magento modal widget. You’ll need to override the template file by creating a new one in your theme with the same path. Then wrap the template content you want in the modal with the magento modal template syntax. You’ll want to add a button or some sort of element that will initialize and load the modal on click.
Here is the magento modal documentation page: https://devdocs.magento.com/guides/v2.3/javascript-dev-guide/widgets/widget_modal.html