Global Zariski main theorem for quasi-finite morphisms of non-Archimedean analytic spaces

Let $k$ be a complete non-Archimedean valued field, and let $f:X\rightarrow S$ be a quasi-finite morphism of quasi-compacted, separated $k$-analytic spaces. We seek a factorization through $k$-analytic spaces $Y$ and $Z$, with morphisms $g:X\rightarrow Y$, $i:Y\rightarrow Z$, and $h:Z\rightarrow S$. Global Zariski main theorem conjecture. The morphism $f$ can be decomposed as

$$f=h\circ i\circ g,$$

where $g$ is finite, $i$ is a quasi-compact analytic domain embedding, and $h$ is étale. This would provide a global analogue of Zariski's main theorem in non-Archimedean geometry. A local version is known for quasi-finite morphisms of separated $k$-analytic spaces, but the global structure of such morphisms remains unresolved.