  Twisted bilayers host many emergent phenomena in which the electronic
excitations (quasiparticles - QPs) are closely intertwined with the local
stacking order. By inspecting twisted hexagonal boron nitride (t-hBN), we show
that non-local long-range interactions in large twisted systems cannot be
reliably described by the local (high-symmetry) stacking and that the band gap
variation (typically associated with the moir\'e excitonic potential) shows
multiple minima with variable depth depending on the twist angle. We
investigate twist angles of 2.45$^\circ$, 2.88$^\circ$, 3.48$^\circ$ and
5.09$^\circ$ using the GW approximation together with stochastic compression to
analyze the QP state interactions. We find that band-edge QP hybridization is
suppressed for intermediate angles which exhibit two distinct local minima in
the moir\'e potential (at AA region and saddle point (SP)) which become
degenerate for the largest system (2.45$^\circ$).
