Recent work has demonstrated that exoplanetary system properties correlate strongly with ambient stellar clustering in six-dimensional stellar position-velocity phase space, quantified by dividing planetary systems into sub-samples with high or low phase space densities (`overdensity and `field systems, respectively). We investigate the physical origins of the phase space overdensities and, thereby, which environmental mechanisms may have impacted the planetary systems. We consider the galactic-scale kinematic structure of the Milky Way observed with Gaia and show that the overdensities correspond to the well-known, kpc-scale kinematic ripples and streams in the Galactic disk, which are thought to be generated by bar and spiral arm-driven resonances and satellite galaxy passages. We also find indications that the planet demographics may vary between individual phase space overdensities, which potentially have differing physical origins and histories. Planetary systems associated with the `phase space spiral (a recent perturbation of the Galactic disk) have a hot Jupiter-to-cold Jupiter ratio that is 10 times higher than in field systems. Finally, the hot Jupiter-to-cold Jupiter ratio within overdensities may increase with host stellar age over Gyr timescales. Because the overdensities persist for several Gyr, we argue that late-time perturbations of planetary systems most likely explain these trends, although additional perturbations at birth may contribute too. This suggests that planetary system properties are not just affected by stellar clustering in their immediate surroundings, but by galaxy-scale processes throughout their evolution. We conclude by discussing the main open questions towards understanding the diversity of physical processes that together set planetary system architectures.
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