Generic stability and connected-component equality for definably compact groups over the Laurent series field

Let $G$ be a definably compact group defined over $\mathbb{C}((t))$. Write $G^0$ for the connected component and $G^{00}$ for the smallest type-definable subgroup of bounded index.

Conjecture on definably compact groups. The group $G$ is generically stable, and

$$G^{00}=G^0$$

is a finite-index subgroup of $G$.

This is the revised conjecture attributed in the source to the work cited as cite{LY}; the source provides no resolution evidence.