If you want to check with hook_form_alter if the taxonomy term is new or updated (old) you can't use the form_id or the $form_state->getFormObject()->getOperation() because it always returns "default". The solution for this is :
$form_state->getFormObject()->getEntity()->isNew()
//So for example:
$form_state->getFormObject()->getEntity()->isNew() ? do_this($form,$form_state) : do_that($form,$form_state);