Invariance of topological entropy under complete metrized field extension

Let $k$ be a complete metrized field, let $X$ be a projective variety defined over $k$, and let $f\colon X\dashrightarrow X$ be a dominant rational map. For any complete metrized field extension $K/k$, let $X_K$ be the base change of $X$ and let $f_K\colon X_K\dashrightarrow X_K$ be the rational self-map induced by base change. Entropy-invariance problem. One asks whether

$$\operatorname{h_{top}}(f_K)=\operatorname{h_{top}}(f).$$

The problem concerns whether the topological entropy defined for rational maps is unchanged after extending the complete metrized ground field. The source presents this as an open problem; for regular maps, the entropy agrees with that of the induced action on the Berkovich analytification.