Abstract: Cosmological first-order phase transitions (FOPT) can occur in a secluded dark sector at relatively late times in the radiation era. Such FOPTs might feature in models addressing the Hubble tension or in sourcing the gravitational wave signal observed in pulsar timing array measurements. Proceeding via stochastic bubble nucleation, these FOPTs generate large scale scalar curvature perturbations that are independent of the microscopic details, and hence provide a post-inflationary source of additional features on the primordial perturbation spectrum. Even through purely gravitational interactions with the Standard Model, these perturbations can impact various cosmological and astrophysical observables. I will discuss how measurements of the CMB, Lyman-alpha, reionization and halo structure can gravitationally constrain these FOPTs across various scales. The perturbation bounds obtained can be stronger than traditional homogeneous energy density constraints on the dark sector. Finally, I will also comment on how these cosmological probes can be applied to other FOPT scenarios that produce warm dark matter or helical magnetic fields.