Frontend post submission editor how to add post format？

You can set the post format using set_post_format(), which in your case, I would do it like so where I set the post format only if the post was successfully updated:

$status = wp_update_post( $submit );

if ( $status && ! is_wp_error( $status ) ) {
    // Replace 'quote' with whatever the format you preferred.
    set_post_format( $status, 'quote' );
}