Keep in mind Polaris is for Admin experiences only in Shopify, not client side/customer facing experiences. The base React stuff that is created when you create the App template is for this Admin experience and cannot be used in the theme-app-extension.
To get a modal to show up after clicking a button on your PDP, you’ll have to create and compile a separate/new React application that works within the confines of your store or use JavaScript and Liquid inside the extension. The later is what is intended to be used with Theme-app extensions so if you can make that work, that would be the way to go.