How do I add a custom captcha to the pop login and register forms?

In your child theme's functions.php add the following:

function ghostpool_custom_captcha() {
    
    /* Validation code goes here */
    
    return $captcha;
}
function ghostpool_custom_captcha_display() {
    
    /* Code to display captcha goes here */
    
}

You will need to get the validation code and display code for the captcha plugin that the plugin website should provide.