By combining ab initio downfolding with cluster dynamical mean-field theory, we study the degree of correlations in monolayer, bilayer, and bulk breathing-mode kagome van der Waals materials Nb₃(F, Cl, Br, I)₈. Our new material-specific many-body model library shows that in low-temperature bulk structures the Coulomb correlation strength steadily increases from I to Br, Cl, and F, allowing us to identify Nb₃I₈ as a weakly correlated insulator whose gap is only mildly affected by the local Coulomb interaction. Nb₃Br₈ and Nb₃Cl₈ are strongly correlated insulators, whose gaps are significantly influenced by Coulomb-induced vertex corrections. Nb₃F₈ is a prototypical bulk Mott insulator whose gap is initially opened by strong correlation effects. Angle-resolved photoemission spectroscopy measurements comparing Nb₃Br₈ and Nb₃I₈ allow us to experimentally confirm these findings by revealing spectroscopic footprints of the degree of correlation. Our calculations further uncover how the thickness and the stacking affect the degree of correlations and predict that the entire material family can be tuned into correlated charge transfer or Mott-insulating phases upon electron or hole doping. Our magnetic property analysis based on our model parameter library additionally confirms that interlayer magnetic interactions likely drive the lattice phase transition to the low-temperature structures. The accompanying bilayer hybridization through interlayer dimerization yields magnetic singlet-like ground states in the Cl, Br, and I compounds. We further prove that all low-temperature compounds are dynamically stable and that electron-phonon coupling to the low-energy subspace is suppressed. Our findings establish Nb₃X₈ as a robust, versatile, and tunable class for van der Waals-based Coulomb and Mott engineering with a rich phase diagram and allow us to speculate on the symmetry-breaking effects necessary for the recently observed Josephson diode effect in NbSe₂/Nb₃Br₈/NbSe₂ heterostructures.