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Evidence for correlated insulating and superconducting phases around regions of high density of states was reported in the strongly spin-orbit coupled van der Waals material twisted tungsten diselenide (tWSe_{2}). We investigate their origin and interplay by using a functional renormalization group approach that allows one to describe superconducting and spin/charge instabilities in an unbiased way. We map out the phase diagram as a function of filling and perpendicular electric field, and find that the moiré Hubbard model for tWSe_{2} features mixed-parity superconducting order parameters with s/f-wave and topological d/p-wave symmetry next to (incommensurate) density-wave states. Our work systematically characterizes competing interaction-driven phases in tWSe_{2} beyond mean-field approximations and provides guidance for experimental measurements by outlining the fingerprint of correlated states in interacting susceptibilities.