Elliott–Halberstam conjecture for friable integers

Let $\varepsilon\in(0,1)$, and let $v=\log x/\log z$ be fixed. Write $\Psi(x',z;a,q)$ for the count of $z$-friable integers up to $x'$ in the reduced residue class $a\pmod q$, and let $\Psi_q(x',z)$ denote the corresponding count with the coprimality condition $(n,q)=1$. Elliott–Halberstam conjecture for friable integers.

$$\sum_{q\leq x^{1-\varepsilon}}\max_{x'\leq x}\;\max_{(a,q)=1}\left|\Psi(x',z;a,q)-\frac{\Psi_q(x',z)}{\varphi(q)}\right|\ll_{A,\varepsilon}\frac{x}{\log^A x}.$$

The implied constant may depend on $A$ and $\varepsilon$. This asserts exponent of distribution $1-\varepsilon$ for friable integers when $v$ is fixed; the source describes it as conjectural, while the preceding discussion mentions partial results of Harper and Pascadi.