Finite generation of lower central series quotients for graph braid groups

Let $UConf_n(\Gamma)$ denote the unordered configuration space of $n$ points on a graph $\Gamma$, and let $\pi(-)$ be the fundamental-group-valued representation $\Gamma\mapsto \pi_1(UConf_n(\Gamma))$ of the opposite graph-minor category. Write $\gamma_i\pi(-)$ for the terms of its lower central series.

Finite generation of LCS quotients. Every successive quotient of the lower central series,

$$\gamma_i \pi(-)/\gamma_{i+1} \pi(-),$$

forms a finitely generated representation of the opposite graph-minor category.

This conjecture asks for finite generation of the graded pieces of graph braid groups under deletion and contraction of graphs. The supplied source does not state whether the conjecture is open or has been resolved.