How to stop media_sideload_image from running when deleting a post?

Question

I believe you can just check if the post status is trash, and if so, don’t run the rest of your code. E.g. (PS: I intentionally used strict comparison, i.e. using === as in $pagenow === 'post.php')

function post_extra_save( $post_id, $post ) {
    global $pagenow;
    if ($pagenow === 'post.php' && 'trash' !== $post->post_status) {
        ... your code.
    }
}

Alternatively, run your code only if the post status is publish or that it’s in one of a whitelisted/allowed statuses list. E.g.

function post_extra_save( $post_id, $post ) {
    global $pagenow;

    $allowed_statuses = array( 'publish', 'private' ); // list of allowed post statuses

    if ($pagenow === 'post.php' && in_array( $post->post_status, $allowed_statuses )) {
        ... your code.
    }
}