You could use the wp_mail function https://developer.wordpress.org/reference/functions/wp_mail/ to send an email to anyone after the file is successfully uploaded in your directory. You do not need any action here
Add it your code after the file is uploaded successfully
if(empty($errors)==true){
move_uploaded_file($file_tmp,"/$user_dirname/".$document);
echo "The file was uploaded successfully!";
wp_mail(..);
}else{
print_r($errors);
}
}