Motivic symplectic cohomology detects smoothly but not symplectically isotopic symplectomorphisms

Let $X$ be a symplectic manifold, and let $g_0,g_1:X\rightarrow X$ be symplectomorphisms. The maps $(g_0)_*$ and $(g_1)_*$ are induced on the groups $SH_{\bullet}^M(Y,X)$ associated with suitable symplectic manifolds $Y$ and $M$. Detection conjecture. If $g_0$ and $g_1$ are smoothly isotopic but not symplectically isotopic, then there exist symplectic manifolds $Y$ and $M$ such that

$$(g_0)_*\neq (g_1)_*.$$

This would provide a way to detect the failure of symplectic isotopy using the motivic symplectic groups. The source states that the problem is still open and that these groups are not yet sufficiently computable for systematic comparisons.