Use this code to add a class to all submit buttons.

add_filter('frm_submit_button_class', 'add_submit_class', 10, 2 );
function add_submit_class( $classes, $form ){
    $classes[] = 'my-custom-class';
    return $classes;
}

Use this code to add a class to a single submit button. Replace 123 with your form ID.

add_filter('frm_submit_button_class', 'add_submit_class', 10, 2);
function add_submit_class( $classes, $form ){
    if ( $form->id == 123 ) {
        $classes[] = 'my-custom-class';
    }
    return $classes;
}

add_filter( 'frm_submit_button_class', 'my_custom_function', 10, 2 );
function my_custom_function( $classes, $form ) {
    global $frm_page_num;

    $target_form_id = '123'; // Replace 123 with the id of the form you need to affect

    if ( $target_form_id === $form->id ) {
        $classes[] = 'submit-button-on-page-' . $frm_page_num;
    }

    return $classes;
}