Waldhausen null-homotopy conjecture for rigid analytic spaces

Let $T$ be an adic ring over $\mathbb{Z}_p$ with a two-sided ideal $I$ such that each $T/I^n$ for $n e 0$ is finite of order a power of $p$. Let $X$ be a rigid analytic space separated and of finite type over $\mathbb{Q}_p$, and suppose that $\mathbb{D}_{\mathrm{perf}}(X_\sharp,T)$ for $\sharp=\text{\'et}$ has a Waldhausen structure and that the Waldhausen exact functor $R\Gamma_?(X_\sharp,.)$, with $?=\emptyset$, is defined.

Waldhausen null-homotopy conjecture. The induced map

$$\mathbb{K}\mathbb{D}_{\mathrm{perf}}(X_\sharp,T)\longrightarrow \mathbb{K}\mathbb{D}_{\mathrm{perf}}(T)$$

is homotopic to the zero map.

This predicts a vanishing phenomenon for the $K$-theory map induced by derived global sections in the $p$-adic setting. The surrounding discussion indicates that the expected proof should use finiteness and cohomological-dimension results, but no proof or resolution is supplied here.