Asymptotically Hölder gradient regularity for degenerate or singular parabolic normalized $ p$-Laplace equations

We study bounded viscosity solutions of the degenerate or singular parabolic equation \[ u_t-|Du|^γΔ_p^{\mathrm{N}}u=f \qquad \text{in } Q_1, \] where \[ Δ_p^{\mathrm{N}}u := Δu+(p-2) \left\langle D^2u\frac{Du}{|Du|}, \frac{Du}{|Du|} \right\rangle, \qquad -1<γ<\infty,\quad 1<p<