  We characterize quantum dynamics in triangular billiards in terms of five
properties: (1) the level spacing ratio (LSR), (2) spectral complexity (SC),
(3) Lanczos coefficient variance, (4) energy eigenstate localisation in the
Krylov basis, and (5) dynamical growth of spread complexity. The billiards we
study are classified as integrable, pseudointegrable or non-integrable,
depending on their internal angles which determine properties of classical
trajectories and associated quantum spectral statistics. A consistent picture
emerges when transitioning from integrable to non-integrable triangles: (1)
LSRs increase; (2) spectral complexity growth slows down; (3) Lanczos
coefficient variances decrease; (4) energy eigenstates delocalize in the Krylov
basis; and (5) spread complexity increases, displaying a peak prior to a
plateau instead of recurrences. Pseudo-integrable triangles deviate by a small
amount in these charactertistics from non-integrable ones, which in turn
approximate models from the Gaussian Orthogonal Ensemble (GOE). Isosceles
pseudointegrable and non-integrable triangles have independent sectors that are
symmetric and antisymmetric under a reflection symmetry. These sectors
separately reproduce characteristics of the GOE, even though the combined
system approximates characteristics expected from integrable theories with
Poisson distributed spectra.
