  We consider an effective Hubbard model with spin- and direction-dependent
complex hoppings $t$, applied to twisted homobilayer WSe$_2$ using a
variational Monte Carlo approach. The electronic correlations are taken into
account by applying the Gutzwiller on-site correlator as well as long-range
Jastrow correlators subjected to noninteracting part being of Pfaffian form.
Our analysis shows the emergence of Mott insulating state at critical value of
Hubbard interaction $U_{c1}\approx 6.5|t|\div7|t|$ estimated by extrapolating
the density-density equal-time two-particle Green's functions. The signatures
of an intermediate insulating phase between $U_{c1}$ and
$U_{c2}\approx9.5|t|\div10|t|$ are also discussed. Furthermore, we report the
formation of the $120^{\circ}$ in-plane N\'eel state indicated by the detailed
analysis of the spin-spin correlation functions. As shown, switching between
antiferromagnetic phases characterized by opposite chirality could be
experimentally realized by the change of perpendicular electric field. In
proper range of electric fields also a transition to in-plane ferromagnetic
state appears.
