The set-palette conjecture for complete graphs

Let $K_n$ be the complete graph on $n$ vertices. In a general edge-coloring of $K_n$, let $\tau_s(n)$ denote the minimum number of colors needed so that all triangles have distinct color palettes when a palette is viewed as the set of colors appearing on its three edges. Set-palette conjecture. For $n\geq4$,

$$\tau_s(n)=n-1.$$

The source notes the inequality $\tau_m(n)\leq\tau_s(n)\leq\tau'(n)$ and states that this conjecture would imply the preceding multiset-palette conjecture. Its status is not resolved in the supplied text.