“With that being said” can be said without saying a thing in most cases. So don’t say it.
A reader or listener does not know the meaning of that instance of “With that being said” till you say the next thing. It adds only the illusion of clarity about what you already said, or your opinion about it, or what will follow.
You already said what you said. There’s no need to say so.
In every case, it is lazy. That is “With that being said” at its level best.
At its worst, “With that being said” reads like a (still lazy) compulsion and adds zero meaning.
When there’s a need to say you are going to ignore, refute, or challenge what you just said, say that. Or just do it.
In spoken English, “With that being said” buys you a moment to decide what to say next. Instead, treat the audience to a pause.
My daughter likes it as a pause and says it adds structure. I think by structure she means meat. It is ground beef, at best.
“With that being said” is an English tic which I have seen infect speakers of every age, not just young people.
I am aware this fashion isn’t going anywhere.