Lose Data fields When Recaptcha is Invalid

If a person types the incorrect Captcha values by mistake, the error results in jumping to a rather primitive error notice page. Why not a simple AJAX pop-up error notice as not to lose the data entered? As a result, the user loses all their data entered, and has to retype all the content over again. Very unprofessional.

As a courtesy, all my PHP forms on each website I design includes:

header("Cache-Control: private, max-age=10800, pre-check=10800");
	header("Pragma: private");
	header("Expires: " . date(DATE_RFC822,strtotime("+1 day")));

This allows the data to be retained, as long as the browser stays in session, even if jumping to another page. Is this not applicable to the functions of this plugin?

https://ww.wp.xz.cn/plugins/google-captcha/