Displaying a button on each post

Use the_content hook and hook only when you are on a single page:

add_filter( 'the_content', 'my_button_function' );

function my_button_function( $content ) {

    // See if it's a single post or a loop
    if ( is_single() && in_the_loop() && is_main_query() ) {
        return $content . "<button onclick=\"buttonAction()\" p style=\"font-size:10px\" id=\"ActionButton\">ACTION</button>";
    }

    return $content;
}

This will only add the button if you are on a single post, and will add the button at the end of your content.

Further reading at : WordPress Developer’s website.