Waring-locus additivity 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 $F=\sum_{i=1}^sF_i\in S_d$, with $d\geq3$. Write $\mathcal{W}_{F_i}$ for the Waring locus of $F_i$, embedded in the corresponding coordinate linear subspace of $\mathbb{P}^N$, where

$$N=n_1+\cdots+n_s+s-1.$$

Waring-locus additivity 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

$$\mathcal{W}_F=\bigcup_{i=1}^r\mathcal{W}_{F_i}\subset\mathbb{P}^N.$$

The conjecture asks whether every point appearing in a minimal Waring decomposition of the sum comes from one of the summands. The source does not specify its resolution status.