I do this with Vue in Symfony PHP apps. Depending on the scope I eitehr have a full build pipeline for the JS (preferred) or will include the files direct from a CDN and have in-HTML templates that are parsed on load.

For passing data into it I've used Inertia.js [0] and also my own data-in-page setup that's parsed and loaded into the Vue app. The app then writes the changes back out, usually into a hidden form input. The form on the page is then submitted as usual to the server, along with any other data that I need.

It's a great way for adding more complicated behaviour to an existing app.

0. https://inertiajs.com/