  We study the electronic structure and correlated phases of twisted bilayers
of platinum diselenide using large-scale ab initio simulations combined with
the functional renormalization group. PtSe$_2$ is a group-X transition metal
dichalcogenide, which hosts emergent flat bands at small twist angles in the
twisted bilayer. Remarkably, we find that moir\'e engineering can be used to
tune the strength of Rashba spin-orbit interactions, altering the electronic
behavior in a novel manner. We reveal that an effective triangular lattice with
a twist-controlled ratio between kinetic and spin-orbit coupling scales can be
realized. Even dominant spin-orbit coupling can be accessed in this way and we
discuss consequences for the interaction driven phase diagram, which features
pronounced exotic superconducting and entangled spin-charge density waves.
