Strassen's decomposition conjecture for disjoint-variable forms

Let $S=\mathbb{C}[x_{1,0},\ldots,x_{1,n_1},\ldots,x_{s,0},\ldots,x_{s,n_s}]$ be the polynomial ring in $s$ disjoint blocks of variables, and let $S^{[i]}=\mathbb{C}[x_{i,0},\ldots,x_{i,n_i}]$. Let $F_i\in S^{[i]}_d$ and set $F=\sum_{i=1}^sF_i\in S_d$, where $d\geq 3$. A minimal Waring decomposition is a decomposition using exactly $\operatorname{rk}(F)$ summands.

Strassen's decomposition conjecture. If $F=\sum_{i=1}^sF_i\in S$ is a degree $d\geq3$ form such that $F_i\in S^{[i]}$ for all $i=1,\ldots,s$, then any minimal Waring decomposition of $F$ is a sum of minimal Waring decompositions of the forms $F_i$.

This is a decomposition-level strengthening of rank additivity for forms in disjoint variables. The source notes that sufficient conditions are known, but does not specify whether the conjecture has been resolved.