Guo and Schlosser's companion q-congruence for d-adic parameters

Let $d\geqslant 3$ and let $n>1$ be an integer with $n\equiv 1\pmod{d}$. With $(a;q)_k=(1-a)(1-aq)\cdots(1-aq^{k-1})$, $[m]=1+q+\cdots+q^{m-1}$, and $\Phi_n(q)$ the $n$-th cyclotomic polynomial, Guo and Schlosser's companion conjecture. For $M=((d-1)n+1)/d$ or $n-1$, one has

$$\sum_{k=0}^{M}[2dk-1] \frac{(q^{-1};q^d)_k^{2d}}{(q^d;q^d)_k^{2d}}q^{d^2 k} \equiv 0 \pmod{[n]\Phi_{n}(q)^3}.$$

The paper subsequently gives a proof of this conjecture, so it is included as a resolved claim rather than an open conjecture.