Getting author’s nickname as meta value

After review, I would expect your code to work properly: to only save the creating author’s nickname, and not override it later.

Here’s some code to try with slight improvements and redundancies (tested):

function data_nickname( $post_id, $post, $update ) {
    // If the post is being updated, bail.
    if ( $update ) {
        return;
    }

    $author_ID = $post->post_author;
    $nickname  = get_the_author_meta( 'nickname', $author_ID );

    // Only set post meta if it doesn't already exist.
    add_post_meta( $post_id, 'data_nickname', $nickname, true );
}
add_action( 'wp_insert_post', 'data_nickname', 10, 3 );

I recommend changing the post meta key to something more clear than data_nickname, like original_authors_nickname. In five years and possibly a different developer, it will then be more clear what it’s purpose is.