The conjecture that the Lusternik–Schnirelmann category of symplectic groups is $2n-1$

For the compact symplectic group $Sp(n)$, let $\operatorname{cat}(Sp(n))$ denote its Lusternik–Schnirelmann category. Symplectic-group category conjecture.

$$\operatorname{cat}(Sp(n))=2n-1\quad\text{for all }n\geq 1.$$

This is described in the source as an old conjecture. The paper proves bounds for $Sp(n)$ when $n\geq 3$ and exact values in low rank, but does not resolve the asserted formula for all $n$.