Keeping post_date same as the pending post_date on privately publishing the post

I’m saving my CPT in private status. So the transition would be from pending to private. Thing is, when the post was first submitted and is pending there’s a date of that submission on the post_date field in db. But when the post got published, the date updated with the current date.

I want to keep the original date of the submission of the post even the post privately published later.

So I did something like below:

function mycpt_keep_pending_date_on_publishing( $new_status, $old_status, $post ) {
    if( 'mycpt' === $post->post_type && 'pending' === $old_status && 'private' === $new_status ) :
        $pending_datetime = get_post_field( 'post_date', $post->ID, 'raw' );

        // Update the post  
        $modified_post = array(  
            'ID'            => $post->ID,  
            'post_date'     => $pending_datetime,
            'post_date_gmt' => get_gmt_from_date( $pending_datetime )
        );  

        // Update the post into the database  
        wp_update_post( $modified_post );

    endif;
}

add_action( 'transition_post_status', 'mycpt_keep_pending_date_on_publishing' );

But it’s not working. What can be the reason?

@Howdy_McGee is on the right track in his comment: by the time transition_post_status is fired, the post has already been updated (i.e., written to the db).

What you need to do is hook into wp_insert_post_data, instead of transition_post_status, as follows:

add_filter ('wp_insert_post_data', 'mycpt_keep_pending_date_on_publishing', 10, 2) ;

function
mycpt_keep_pending_date_on_publishing ($data, $postarr)
{
    if ($data['post_type'] != 'mycpt') {
        return ($data) ;
        }

    // this check amounts to the same thing as transition_post_status(private, pending)
    if ('private' != $data['post_status'] || 'pending' != $postarr['original_post_status']) {
        return ($data) ;
        }

    $pending_datetime = get_post_field ('post_date', $data['ID'], 'raw') ;

    $data['post_date'] = $pending_datetime ;
    $data['post_date_gmt'] = get_gmt_from_date ($pending_datetime) ;

    return ($data) ;
}

Note: I used the same function name as you did, but the body of that function is different.