In-plane resistivity ${\ensuremath{\rho}}_{\ensuremath{\parallel}}$ and out-of-plane resistivity ${\ensuremath{\rho}}_{\ensuremath{\perp}}$ were investigated across the pressure-induced Mott transition in molecular Mott insulators $Z{[\mathrm{Pd}{(\mathrm{dmit})}_{2}]}_{2}$ ($Z={\mathrm{Et}}_{2}{\mathrm{Me}}_{2}\mathrm{As}$, ${\mathrm{Me}}_{4}\mathrm{N}$, and ${\mathrm{EtMe}}_{3}\mathrm{P}$) having a triangular lattice. All three compounds exhibit superconducting transition with ${T}_{c}=5.5--7.0$ K in the metallic phase near the Mott insulating phase. For the ${\ensuremath{\beta}}^{\ensuremath{'}}\text{\ensuremath{-}}{\mathrm{Et}}_{2}{\mathrm{Me}}_{2}\mathrm{As}$ salt, the anisotropy ${\ensuremath{\rho}}_{\ensuremath{\perp}}/{\ensuremath{\rho}}_{\ensuremath{\parallel}}$ exceeds ${10}^{3}$ at low temperatures, indicating a highly two-dimensional electronic state with incoherent interlayer hopping. The $\ensuremath{\beta}\text{\ensuremath{-}}{\mathrm{Me}}_{4}\mathrm{N}$ salt has a smaller ${\ensuremath{\rho}}_{\ensuremath{\perp}}/{\ensuremath{\rho}}_{\ensuremath{\parallel}}$ exhibiting a weak interlayer coupling. The resistivity is dominated by electron-electron scattering in the metallic state for these two compounds, as expected in a correlated Fermi liquid. On the other hand, the ${\mathrm{EtMe}}_{3}\mathrm{P}$ salt with a valence bond order state becomes a nearly three-dimensional metal across the Mott transition, in which the electron correlation is strongly suppressed. Instead, the electron-phonon scattering plays a significant role in the resistivity. The different interlayer coherence is quantitatively explained by the calculated interlayer transfer integrals between $\mathrm{Pd}{(\mathrm{dmit})}_{2}$ molecules. These results suggest that the dimensionality governs the nature of electron correlations in the Fermi liquid state.