callback function and class in shortcode

What do you want to do? To redefine the shortcode fully?

You can simply use the statement:

add_shortcode( 'cf7-hcaptcha', [ $this, 'my_cf7_hcaptcha_shortcode' ] );

after \HCaptcha\CF7 class initialization, which happens on plugins_loaded action with the earliest priority: -PHP_INT_MAX.

So, you can add your own shortcode like this

class My_CF7_Shortcode {

	public function __construct() {
		add_action( 'plugins_loaded', [ $this, 'add_shortcode' ] );
	}

	public function add_shortcode() {
		add_shortcode( 'cf7-hcaptcha', [ $this, 'my_cf7_hcaptcha_shortcode' ] );
	}

	public function my_cf7_hcaptcha_shortcode() {
		// Do something...
	}
}

This will redefine shortcode by itself, but all the processing (verification) will still work from the hCaptcha plugin.