Recent experiments in twisted bilayer transition-metal dichalcogenides have revealed a variety of strongly correlated phenomena. To theoretically explore their origin, we combine here ab initio calculations with correlated model approaches to describe and study many-body effects in twisted bilayer WSe₂ under pressure. We find that the interlayer distance is a key factor for the electronic structure, as it tunes the relative energetic positions between the K and the Γ valleys of the valence band maximum of the untwisted bilayer. As a result, applying uniaxial pressure to a twisted bilayer induces a charge-transfer from the K valley to the flat bands in the Γ valley. Upon Wannierizing moiré bands from both valleys, we establish the relevant tight-binding model parameters and calculate the effective interaction strengths using the constrained random phase approximation. With this, we approximate the interacting pressure-doping phase diagram of WSe₂ moiré bilayers using self-consistent mean field theory. Our results establish twisted bilayer WSe₂ as a platform that allows the direct pressure-tuning of different correlated phases, ranging from Mott insulators, charge-valley-transfer insulators to Kondo lattice-like systems.