Following 4.6 and 4.7 of this paper by Seidel and Thomas, a graded algebra $A$ is called intrinsically formal if any two dgas with cohomology $A$ are quasi-isomorphic. There is a sufficient condition that says for an augmented graded algebra $A$, if the Hochschild cohomology $HH^q(A, A[2 − q]) = 0$ for all $q > 2$, then $A$ is intrinsically formal.

Is it possible to verify this condition for the exterior algebra on a vector space $V$? To be clear, it could be either $Sym(V[1])$ or $Sym(V[-1])$. The characteristic and the dimension of $V$ might be important. I'm focusing on char$=0$ or $2$ and dimensions $1$ and $2$.

There is a related question on the computation, but I'm not sure if the answer is enough to verify the condition. There are also related papers 1 2 3, but all of them seem to deal with the exterior algebra as an ungraded algebra.