Twisted Ratios conjecture for Dirichlet $L$-functions

Let $r$ be a prime, let $\chi_0$ be the principal character modulo $r$, and let $f$ be a completely multiplicative function with $f^*(n)=f(n)\mathbf 1_{\operatorname{gcd}(n,r)=1}$ and $L^*(s,f)=\prod_{p\ne r}(1-f(p)p^{-s})^{-1}$. Let $\Re(s_1)=\Re(s_2)=\frac12+\varepsilon$, let $1\leq m_1,m_2\leq r^\hbar$, and put $T=\max(|\Im s_1|,|\Im s_2|)$. Twisted Ratios conjecture. If $\varepsilon,\hbar>0$ are sufficiently small, then for some absolute constant $\omega'\in(0,\frac12]$, independent of $r,\varepsilon,\hbar$,

$$\mathbb E_{\chi\ne\chi_0}\frac{\chi(m_1)\overline\chi(m_2)}{L(s_1,\chi)L(s_2,\overline\chi)}=\mathbb E_f\frac{f^*(m_1)\overline{f^*(m_2)}}{L^*(s_1,f)L^*(s_2,\overline f)}+O_\varepsilon((1+T)^\varepsilon r^{-\omega'}).$$

This twisted form is presented as an implication of the usual Ratios Conjecture and would support the paper's estimates in ranges where character orthogonality is unavailable. The source does not establish it.