This paper presents a study of the two-dimensional Yukawa-Sachdev-Ye-Kitaev (2d-YSYK) model, which describes quantum phase transitions in metals with quenched random spatial fluctuations near the quantum critical point. The model couples fermions with a Fermi surface to a scalar field via spatially random Yukawa interactions. The authors perform full numerical solutions of the self-consistent disorder-averaged equations for both the normal and superconducting states, obtaining electronic spectral functions, frequency-dependent conductivity, and superfluid stiffness. Their results reproduce key observations in cuprate superconductors, including the behavior of the superfluid stiffness as a function of the superconducting critical temperature. The paper also explores the behavior of strange metals, which are metallic phases where the Landau quasiparticle approach breaks down. These metals exhibit a linear-in-temperature electrical resistivity. The authors analyze the optical conductivity of the 2d-YSYK model and find that it matches the observed behavior in cuprate superconductors, including the non-Drude power-law tail in the optical conductivity and the Planckian scaling of the transport scattering rate. The 2d-YSYK model is shown to exhibit a number of experimentally observed trends, including a monotonic relation between the superconducting critical temperature and the slope of the linear-T resistivity, an overdoped regime where decreasing Tc is accompanied by increasing T=0 superfluid density, and a connection between the T=0 superfluid density and the normal state conductivity at Tc similar to Homes' Law. The paper also discusses the instability of the strange metal to superconductivity, with the pairing type depending on the particular quantum phase transition being studied. The authors examine an instability to spin-singlet pairing in a simplified model and find that the 2d-YSYK model exhibits a number of experimentally observed trends, including the behavior of the superfluid stiffness as a function of the superconducting critical temperature. The authors also discuss the role of spatially random interactions in the 2d-YSYK model and show that the model can be used to describe the behavior of strange metals and superconductors in cuprates. The paper concludes with a discussion of the implications of the results for the understanding of quantum phase transitions in metals and the role of disorder in these systems.This paper presents a study of the two-dimensional Yukawa-Sachdev-Ye-Kitaev (2d-YSYK) model, which describes quantum phase transitions in metals with quenched random spatial fluctuations near the quantum critical point. The model couples fermions with a Fermi surface to a scalar field via spatially random Yukawa interactions. The authors perform full numerical solutions of the self-consistent disorder-averaged equations for both the normal and superconducting states, obtaining electronic spectral functions, frequency-dependent conductivity, and superfluid stiffness. Their results reproduce key observations in cuprate superconductors, including the behavior of the superfluid stiffness as a function of the superconducting critical temperature. The paper also explores the behavior of strange metals, which are metallic phases where the Landau quasiparticle approach breaks down. These metals exhibit a linear-in-temperature electrical resistivity. The authors analyze the optical conductivity of the 2d-YSYK model and find that it matches the observed behavior in cuprate superconductors, including the non-Drude power-law tail in the optical conductivity and the Planckian scaling of the transport scattering rate. The 2d-YSYK model is shown to exhibit a number of experimentally observed trends, including a monotonic relation between the superconducting critical temperature and the slope of the linear-T resistivity, an overdoped regime where decreasing Tc is accompanied by increasing T=0 superfluid density, and a connection between the T=0 superfluid density and the normal state conductivity at Tc similar to Homes' Law. The paper also discusses the instability of the strange metal to superconductivity, with the pairing type depending on the particular quantum phase transition being studied. The authors examine an instability to spin-singlet pairing in a simplified model and find that the 2d-YSYK model exhibits a number of experimentally observed trends, including the behavior of the superfluid stiffness as a function of the superconducting critical temperature. The authors also discuss the role of spatially random interactions in the 2d-YSYK model and show that the model can be used to describe the behavior of strange metals and superconductors in cuprates. The paper concludes with a discussion of the implications of the results for the understanding of quantum phase transitions in metals and the role of disorder in these systems.