  To establish a solid-state-based framework for the coexistence of quantum
many-body scars and quantum criticality, we investigate the spin-1 Kitaev chain
with uniaxial single-ion anisotropy (SIA). In the subspace with uniform
$\mathbb{Z}_2$ gauge fields, this model can be exactly mapped to the spin-1/2
effective detuned PXP Hamiltonian, where the SIA plays a role of the static
detuning term. The quench dynamics starting from the product states is
symmetric between positive and negative values of the SIA, while a quantum
phase transition from the Kitaev spin liquid to the dimer phase only occurs at
the critical point with a negative $D_c$, implying the spontaneous breaking of
the translational symmetry. We find that the coherent oscillations of quantum
fidelity and certain local observables are sustained against small SIA
perturbations in a quantum quench from special initial states. While the
oscillation amplitudes of these observables decay with time as the SIA strength
is increased, the system completely thermalizes upon approaching the critical
point. In contrast, the initial polarized state, which shows an absence of
revivals of quantum fidelity, will exhibit long revivals for $D<D_c$. Finally,
we investigate the evolution of phase boundaries of the Kitaev spin liquid and
dimer phase by introducing Heisenberg interactions, which spoil the
$\mathbb{Z}_2$ gauge fields. A complete phase diagram is given by the infinite
time-evolving block decimation method and the ground state properties of each
phase are accurately captured by various spin correlations. Our work opens the
door to understanding exotic connections between many-body scars and quantum
criticality in systems with higher spins.
