How to generate frontend page with callback?

I solved it with the help of @PatJ’s comment.

    add_filter('the_content', function ($content) use ($callback){
        if (is_singular() && in_the_loop() && is_main_query()){
            $id = get_the_ID();
            if (in_array($id, array_values($this->pages))){
                ob_start();
                $callback();
                return ob_get_clean();
            }
        }
        return $content;
    }, 1);

Note that in this solution the headers are already sent and only rendering is possible. If we want to send for example a location header to redirect the page, then we need a different solution, which is:

add_action('init', function (){
    $id = url_to_postid($_SERVER['REQUEST_URI']);
    if (in_array($id, array_values($this->pages)))
        $callback();
});

So for example in the init we can do redirection if it is a POST and in the_content we can do rendering if it is a GET request.