Guggiari's path-cover conjecture for 2-edge-coloured complete symmetric digraphs

Let $\vec{K}_{\mathbb{N}}$ be the complete symmetric digraph on the positive integers, and let a 2-edge-colouring assign one of two colours, red or blue, to every directed edge. A directed path is a finite or one-way infinite sequence of distinct vertices in which each consecutive pair is joined by a directed edge in the forward direction. Fix $\ell\in\mathbb{N}$. Guggiari's conjecture. If the colouring contains no red directed path of length $\ell$, then the vertices of $\vec{K}_{\mathbb{N}}$ can be covered by at most $\ell$ vertex-disjoint blue directed paths. This would give a sharp path-cover consequence of forbidding a red directed path of prescribed length; the supplied text attributes the conjecture to Guggiari but gives no resolution status, so it remains open here.