WordPress function to run when a scheduled post is published, to change the modified date/time to match. Currently, it will only show the last saved data, not its published information, unless you modify it after publishing.

scheduled_post_modified_date.php

<?php
// Scheduled posts should update modified date when published
function update_modified_date_to_post_date( $post ) {
    $updated_data = [
        'ID'                => $post->ID,
        'post_modified'     => $post->post_date,
        'post_modified_gmt' => $post->post_date_gmt
    ];
    wp_update_post( $updated_data );
}
add_action( 'future_to_publish', 'update_modified_date_to_post_date', 10, 1 );