The goal of this talk is to explain a concrete instance of the theory of non-semisimple TQFT in three dimensions, as discussed in the talk of Nathan Geer in this seminar on Feb. 22nd, 2023. I will describe a recent construction of a TQFT which realizes Chern-Simons theory with gauge supergroup $U(1 \vert 1)$, as studied in the physics literature by Rozansky–Saleur and Mikhaylov. In particular, I'll describe various relative modular structures on the category of representations of the quantum group of $\mathfrak{gl}(1 \vert 1)$ which should be seen as non-semisimple analogues of modular tensor categories associated to the quantum representation theory of a simple Lie algebra at a root of unity. Based on joint work with Nathan Geer.