Guo–Schlosser–Zudilin's divisibility conjecture for sums of even powers of q-binomial coefficients

Let $n$ be a positive integer and let $r$ be an arbitrary integer. Write $[n]=(1-q^n)/(1-q)$ for the $q$-integer and let $\Phi_n(q)$ denote the $n$th cyclotomic polynomial. For integers $a$ and $b$, let $\begin{bmatrix}a\\b\end{bmatrix}_q$ denote the $q$-binomial coefficient. Guo–Schlosser–Zudilin's conjecture.

$$\sum_{k=0}^{n-1}q^{r(n-k)^2+(r-1)k}\begin{bmatrix}n+k\\k\end{bmatrix}_q^{2r}\begin{bmatrix}n-1\\k\end{bmatrix}_q^{2r} \equiv q^{(r-1)n+1}[n]-\frac{r(2r-1)(n-1)^2q(1-q)^2}{4}[n]^3\pmod{[n]\Phi_n(q)^3}.$$

This conjecture unifies earlier conjectures of Gu and Guo and of Guo, Schlosser and Zudilin; the supplied context states that the corresponding congruence modulo $[n]\Phi_n(q)^2$ was still open, and gives no resolution of this stronger modulo $[n]\Phi_n(q)^3$ claim.