  In this paper, we derive lattice models for the narrow moir\'e bands of the
AB-stacked twisted WSe$_2$ homobilayer through continuum model and Wannier
orbital construction. Previous work has shown that an approximate SU(4) Hubbard
model may be realized by combining spin and layer because inter-layer tunneling
is suppressed due to spin $S_z$ conservation. However, Rashba spin-orbit
coupling (SOC) was ignored in the previous analysis. Here, we show that a
Rashba SOC of reasonable magnitude can induce a finite but very small
inter-layer hopping in the final lattice Hubbard model. At total filling $n=1$,
we derive a spin-layer model on a triangular lattice in the large-U limit where
the inter-layer tunneling contributes as a sublattice-dependent transverse
Ising field for the layer pseudospin. We then show that the $n=2$ Mott
insulator is also captured by an approximate SU(4) spin model, but now on
honeycomb lattice. We comment on the possibility of a Dirac spin liquid (DSL)
and competing phases due to SU(4) anisotropy terms.
