Tong-Viet's quasi-simple-group conjecture for Brauer character degrees

Let $G$ be a finite quasi-simple group with centre $Z(G)$ of $p'$-order. Let $\operatorname{IBr}(G\mid\theta)$ denote the irreducible $p$-Brauer characters of $G$ lying over $\theta$, and let $\operatorname{Irr}(Z(G))$ denote the ordinary irreducible characters of $Z(G)$. Tong-Viet's conjecture. For all faithful characters $\theta\in\operatorname{Irr}(Z(G))$,

$$|G/Z(G)|_{p'}\leq\sum_{\varphi\in\operatorname{IBr}(G\mid\theta)}\varphi(1)^2.$$

This is a strengthening whose validity for all quasi-simple groups would imply Willems' conjecture for all finite groups. The source uses this reduction and verifies it for certain families and odd primes, but the conjecture is not resolved in general.