What does "that said" mean? It looks like "that" is a subject and "said" is a verb. So it raises a question: what did "that" say? On the other hand, "that being said" is perfectly clear.

"That being said" is a great phrase you can use as a transition device, and it certainly has a level of formality that's appropriate for IELTS writing. "That said" is a bit terse, and could be perceived as a little more informal in tone. As an alternative, I would recommend that you consider using "having said that."