  Twistronic van der Waals heterostrutures offer exciting opportunities for
engineering optoelectronic properties of nanomaterials. Here, we use multiscale
modeling to study trapping of charge carriers and excitons by ferroelectric
polarisation and piezoelectric charges by domain structures in twistronic
WX$_2$/MoX$_2$ bilayers (X=S,Se). For almost aligned 2H-type bilayers, we find
that holes and electrons are trapped in the opposite -- WMo and XX (tungsten
over molybdenum {\it versus} overlaying chalcogens) -- corners of the honeycomb
domain wall network, swapping their position at a twist angle $0.2^{\circ}$,
with XX corners providing $30$\,meV deep traps for the interlayer excitons for
all angles. In 3R-type bilayers, both electrons and holes are trapped in
triangular "3R stacking" domains, where WX$_2$ chalcogens set over MoX$_2$
molybdenums, which act as $130$\,meV deep quantum boxes for interlayer excitons
for twist angles $\lesssim 1^{\circ}$, for larger angles shifting towards
domain wall network XX stacking sites.
