Let $X$ be a preperfectoid space over $\mathrm{Spa}(\mathbb{Q}_p,\mathbb{Z}_p)$. It has several associated sites, with successively finer topologies: $$X_{an} \subset X_{et} \subset X_{proet} \subset X_v.$$

I was wondering: **what is the relationship between vector bundles on these different sites**? Here, by a vector bundle I mean a locally finite free $\mathcal{O}_X$-sheaf for $X_{an}, X_{et}$ and $X_v$, and a locally finite free $\widehat{\mathcal{O}}_X$-sheaf for $X_{proet}$.

If $X$ is perfectoid, it is known that the categories of vector bundles on all of these sites are equivalent, by Theorem 3.5.8 of Kedlaya-Liu's paper "Relative p-adic Hodge Theory II".

Is this also true for preperfectoid spaces? What about sousperfectoid spaces? If this statement is not true, is it still true that some of these categories are equivalent? I expect that at the very least the pullback functor from $X_{an}$ to $X_v$ is fully faithful. My apologies if there is some silly counterexample.

Thanks!