Kollár–Takagi–Tanaka–Witaszek–Yasuda–Yoshikawa log-resolution lifting conjecture for log del Pezzo pairs

Let $(X,\Delta)$ be a log del Pezzo pair over a perfect field of characteristic $p>5$, with standard coefficients. A log resolution is a resolution $f\colon Y\to X$ such that the relevant boundary and exceptional divisors have simple normal crossings. Then there exists a log resolution $f\colon Y\to X$ of $(X,\Delta)$ such that the pair

$$\left(Y,f^{-1}_*\Delta+\operatorname{Exc}(f)\right)$$

lifts to $W(k)$, the ring of Witt vectors of the field $k$. Kollár–Takagi–Tanaka–Witaszek–Yasuda–Yoshikawa's conjecture. Every such pair admits a log resolution whose resolved pair lifts to the Witt vectors. This conjecture is recalled from the cited source; the supplied text gives no resolution status.