Kaneko–Kano–Suzuki conjecture on rainbow spanning trees in proper colourings

Let $K_n$ be a complete graph with a proper edge-colouring, meaning that any two incident edges have different colours. A subgraph is rainbow if all its edges have distinct colours, and edge-disjoint subgraphs share no edges. Kaneko–Kano–Suzuki conjecture. For all $n>4$, every properly edge-coloured $K_n$ contains $\floor{n/2}$ edge-disjoint rainbow spanning trees. This generalizes the Brualdi–Hollingsworth setting from $1$-factorizations to arbitrary proper edge-colourings. The source describes linear-size and asymptotic progress, but does not state that the exact conjecture is proved in full.