As requested by the question-asker, here is my comment copied into an answer:
Let me use $B_n$ for the finite Boolean lattice of subsets of $[n]$ (your $\mathcal{P}(S)$), and let $k=|T|$. Then your $A=\overline{B}_k \times B_{n-k}$, where $\overline{B}_k = B_k \setminus \{\hat{0},\hat{1}\}$ (we remove the minimum and maximum). Since $B_{n-k}$ is contractible (it has a minimum and maximum), taking the product with it does not chance the homotopy type, so indeed $|A| \simeq |\overline{B}_k| \simeq \mathbb{S}^{k-2}$ as you guessed. A good reference for this stuff is "Poset Topology: Tools and Applications" by Michelle Wachs.