The PHANGS-ALMA view of the molecular gas distributions on 150-pc scales within nearby galaxies reveals bright, dense filamentary and clumpy features that coordinate into larger-scale structures echoing the global bar/spiral morphology of each galaxy. This signifies that both gas self-gravity and the background host potential are influential in shaping cloud-scale molecular gas distributions. We quantify this by dividing each galaxy into radial bins and measuring molecular gas surface density contrasts, defined as the ratio between a fixed high percentile of the CO distribution and a fixed reference level in a given radial bin. We compare these contrasts to matched percentile-based measurements of the 3.6 micron emission measured using Spitzer/IRAC images that trace the underlying stellar mass density. We find that the CO contrasts on 150 pc scales are positively correlated with the 3.6 micron contrasts probing smooth non-axisymmetric stellar bar and spiral structures. The correlation appears steeper than linear, consistent with the compression of gas as it flows supersonically in response to large-scale stellar structures, even in the presence of weak or flocculent spiral arms. Our results suggest that stellar dynamical features play an important role in setting the cloud-scale gas density in our galaxies, with gas self-gravity acting as a secondary influence on the 150 pc-scale distribution of gas densities.