hook on the_excerpt

You can write your three_dots function like this:

function three_dots($excerpt) {
    // Append the dots to the existing excerpt.
    $excerpt .= ' [...]';
    return $excerpt;
}
add_filter('the_excerpt', 'three_dots');

About your ‘read more’ button, this usually isn’t handled by the excerpt itself but is instead added after the excerpt in your theme’s template files. If you’ve got a custom ‘read more‘ button, you’d typically place it in your theme’s template file where you’re displaying the excerpt. You can just mod

For instance, in one of your template file, you might have something like:

echo get_the_excerpt();
// Here comes your custom 'read more' button
echo '<a href="' . get_permalink() . '" class="read-more-button">Read More</a>';