  A common wisdom posits that transports of conserved quantities across clean
nonintegrable quantum systems at high temperatures are diffusive when probed
from the emergent hydrodynamic regime. We show that this empirical paradigm may
alter if the strong interaction limit is taken. Using Krylov-typicality and
purification matrix-product-state methods, we establish the following
observations for the strongly interacting version of the mixed-field Ising
chain, a nonintegrable lattice model imitating the experimental Rydberg
blockade array. Given the strict projection owing to the infinite
density-density repulsion $V$, the chain's energy transport in the presence of
a transverse field $g$ is superdiffusive at infinite temperature featured by an
anomalous scaling exponent $\frac{3}{4}$, indicating the existence of a novel
dynamical universality class. Imposing, in addition, a growing longitudinal
field $h$ causes a drastic factorization of the whole Hilbert space into
smaller subsectors, evidenced by the spectral parsing of the eigenstate
entanglement. Being a consequence of this approximate symmetry, a
superdiffusion-to-ballistic transport transition arises at $h\approx g$.
Interestingly, all the above results persist for large but finite interactions
and temperatures, provided that the strongly interacting condition $g,h\ll
k_\textrm{B}T\ll V$ is fulfilled. Our predictions are verifiable by current
experimental facilities.
