Swept shock-wave/turbulent-boundary-layer interactions (STBLIs) exhibit key dynamical differences from their spanwise-homogeneous counterparts, including the suppression of a dominant mechanism of low-frequency unsteadiness. An extensive database of wall-resolved simulations is constructed to examine the differences between the properties of spanwise-homogeneous, swept, and compound swept interaction classes. A novel method for calculating the dynamic linear response of these unsteady flows is also presented, which allows for the identification and characterization of absolute instabilities in the time-resolved turbulent flow, and the ramifications for STBLI dynamics are discussed. The spanwise homogeneous interaction exhibits an absolute instability that is well-correlated with the prominent band of low-frequency unsteadiness, whereas an absolute instability is not present in the simple swept interaction, which exhibits a muted low-frequency band. Further, a relationship between interaction symmetry, separation topology, and low-frequency unsteadiness is described, in which the prominent low-frequency unsteadiness is spatially associated with surface-flow singular points that function to topologically close the separation. For swept interactions, the ramifications of quasi-conical interaction symmetry on the frequency scaling of the shear layer bands are also discussed. In essence, the shear layers of the swept interactions exhibit a mix between classical and conical free-interaction scaling in both mean flow and frequency content.