Virtual split-solvability of dfg groups over $\mathbb{C}((t))$

Let $G$ be a dfg group defined in $\mathbb{C}((t))$, where dfg denotes the property used by the source.

Split-solvability conjecture. The group $G$ is virtually a $\mathbb{C}((t))$-split solvable algebraic group.

This is stated among the source's conjectures, and no proof or disproof is given there.