$\widehat{Z}$ invariants of 3-manifolds were introduced in the physics literature by Gukov, Pei, Putrov and Vafa in the context of supersymmetric gauge theory with the goal of categorifying the Reshetikhin --Turaev invariants of 3-manifold. $\widehat{Z}$ invariants depend on the input data of a Lie superalgebra and some discrete geometric data on the 3-manifold, such as a Spin-$c$ structure. The goal of this talk is to explain a connection between $\widehat{Z}$ invariants and 3-manifold invariants associated to non-semisimple categories of representations of quantum supergroups. Based on work with Francesco Costantino, Matthew Harper and Adam Robertson.