  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 to describe superconducting and spin/charge instabilities in an
unbiased way. We map out the phase diagram as function of filling and
perpendicular electric field, and find that the moir\'e 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.
