Gaining a deeper understanding of the nucleon structure remains one of the longstanding challenges of current hadron physics. This work presents an analysis of transverse-spin dependent azimuthal asymmetries in the Drell--Yan process, $\pi^{-} + \mathrm{p^{\uparrow}} \rightarrow \gamma^{*} + \mathrm{X} \rightarrow \mu^{+} + \mu^{-} + \mathrm{X}$, based on data collected by the Common Muon\allowbreak{} and Proton Apparatus\allowbreak{} for Structure\allowbreak{} and Spectroscopy (COMPASS) Collaboration in 2015 and 2018. The data were obtained using a 190~GeV negative pion beam scattered off transversely polarised NH$_3$ target. The analysis introduces a new method of weighting asymmetries by powers of the dimuon pair transverse momentum relative to the beam. This technique provides direct access to certain $k_{\rm T}^2$ moments of the transverse-momentum dependent parton distribution functions. These findings represent one of the most significant experimental advances in spin physics in recent years and are expected to remain a key reference point until new data from CLAS12, EIC, and LHCspin are available.