Yang–Zeng–Zhang's conjecture for expanded cliques with bounded matching number

Let $K^{(r)+}_{\ell+1}$ be the $r$-uniform expansion of the complete graph on $\ell+1$ vertices, let $M^{(r)+}_{s+1}$ be an $r$-uniform matching with $s+1$ edges, and let $t_{r-1}(n-s,\ell-1)$ denote the number of edges in the complete balanced $(\ell-1)$-partite $(r-1)$-graph on $n-s$ vertices. Yang–Zeng–Zhang's conjecture. For integers $\ell\ge r\ge3$ and $s\ge\binom{\ell}{2}$, and for sufficiently large $n$,

$$\mathrm{ex}_r\left(n,\{K_{\ell+1}^{(r)+},M_{s+1}^{(r)+}\}\right)=s\cdot t_{r-1}(n-s,\ell-1).$$

This is the proposed hypergraph analogue of the Alon–Frankl theorem; the supplied text gives no resolution.