Fractional Erdős matching conjecture

Let $f_0^s(\ell,m)$ be the smallest integer $m'$ such that every $m$-vertex $ell$-uniform hypergraph with minimum $0$-degree at least $m'$ has a fractional matching of size $s$, and set $s=(m+d)/(\ell+d)$.

Fractional Erdős matching conjecture. For integers $\ell,d\geq1$,

$$\limsup_{m\to\infty}\frac{f_0^s(\ell,m)}{\binom{m}{\ell}}\leq1-\left(1-\frac{1}{\ell+d}\right)^\ell.$$

This is described as a fractional version of the Erdős matching conjecture and as sufficient, via a reduction, to establish the fractional perfect matching threshold conjecture. The supplied text gives partial cases but does not state a complete resolution.