  Twistronic assembly of 2D materials employs the twist angle between adjacent
layers as a tuning parameter for designing the electronic and optical
properties of van der Waals heterostructures. Here, we study how interlayer
hybridization, weak ferroelectric charge transfer between layers, and
piezoelectric response to deformations set the valence and conduction band
edges across the moir{\'e} supercell in twistronic homobilayers of MoS$_2$,
MoSe$_2$, WS$_2$ and WSe$_2$. We show that, due to the lack of inversion
symmetry in the monolayer crystals, bilayers with parallel (P) and
anti-parallel (AP) unit cell orientations display contrasting behaviors. For
P-bilayers at small twist angles we find band edges in the middle of triangular
domains of preferential stacking. In AP-bilayers at marginal twist angles
($\theta_{AP} < 1^\circ$) the band edges are located in small regions around
the intersections of domain walls, giving highly localized quantum dot states.
