How can I use React packages with the clasic editor?

I solved this by reading from the DOM. Not the prettiest way but it does what I needed.

const CustomUpdateComponent = {...};

document.addEventListener('DOMContentLoaded', () => {
    // replace update button with our own
    const publishingActionButton = document.querySelector( '#publishing-action' );

    if (publishingActionButton) {
        const postId = document.querySelector( '#post_ID' ).value;
        render( <CustomUpdateComponent post={postId} ... />, publishingActionButton );
    }
});