  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 WSe$_2$
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 $\Gamma$ 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 $\Gamma$ valley.
Upon Wannierizing moir\'e 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 WSe$_2$ moir\'e
bilayers using self-consistent mean field theory. Our results establish twisted
bilayer WSe$_2$ 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.
