Power-saving sieve bound for quadratic Hecke sums

Let $(\varphi_k)_k$, $(Q_k)_k$, and $(f_k)_k$ satisfy the hypotheses of the quadratic Hecke-sum conjecture: the forms $\varphi_k$ are non-dihedral, the $Q_k$ are irreducible integer-valued quadratic polynomials, and the Sobolev norms of $f_k$ satisfy $\mathcal{S}_N(f_k)\ll_N1$ for every fixed $N$. Power-saving sieve conjecture. There exists $\delta>0$ such that

$$\frac{\sum_n\left|\lambda_{\varphi_k}(|Q_k(n)|)f_k(n/k)\right|}{kL(\operatorname{ad}\varphi_k,1)}\ll_{\varepsilon}\|Q_k\|^{\operatorname{O}(1)}(\log k)^{-\delta}.$$

The estimate would strengthen the unconditional logarithmic bound and provide a power saving, but the source states that no such improvement is currently known unconditionally.