How to allow more HTML tags in comment for a certain comment_type

This is untested but should work since it gives you the data you need to work from and runs prior to the pre_comment_content filter where the comment is sanitized.

add_filter( 'preprocess_comment', 'wpse_340526_preprocess_comment' );

function wpse_340526_preprocess_comment( $commentdata ) {
    if( 'wpse_response' === $commentdata['comment_type'] ){
        global $allowedtags;
        $allowedtags['pre'] = array('class'=>array());
        $allowedtags['h2'] = array();
        $allowedtags['h3'] = array();
        $allowedtags['h4'] = array();
        $allowedtags['h5'] = array();
        $allowedtags['h6'] = array();
        $allowedtags['ul'] = array();
        $allowedtags['ol'] = array();
        $allowedtags['li'] = array();
    }

    return $commentdata;
}