A Dwork-type q-supercongruence for n congruent to 1 modulo 4

Let $n\equiv 1\pmod{4}$ be a positive integer and let $r\geqslant 1$. Write $(a;q)_k$ for the $q$-shifted factorial, $[m]=(1-q^m)/(1-q)$, and let $\Phi_m(q)$ denote the $m$th cyclotomic polynomial. The Dwork-type q-supercongruence. Modulo

$$[n^r]\prod_{j=1}^r\Phi_{n^j}(q)^2,$$

where $d=1$ or $d=2$,

$$\sum_{k=0}^{(n^r-1)/d}[6k+1]\frac{(q;q^{4})_k(q;q^2)_k^3}{(q^2;q^2)_k(q^{4};q^{4})_k^3}q^{k^2+k} \equiv \frac{(q^2;q^4)_{(n^r-1)/4}(q^{4n};q^{4n})_{(n^{r-1}-1)/4}} {(q^4;q^4)_{(n^r-1)/4}(q^{2n};q^{4n})_{(n^{r-1}-1)/4}}[n]q^{(1-n)/4} \times\sum_{k=0}^{(n^{r-1}-1)/d}[6k+1] \frac{(q^{n};q^{4n})_k(q^n;q^{2n})_k^3}{(q^{2n};q^{2n})_k(q^{4n};q^{4n})_k^3}q^{(k^2+k)n}.$$

This is proposed as a Dwork-type extension of earlier $q$-supercongruences. The surrounding text attributes related work to the author and Zudilin and notes a similar conjecture of Liu and Wang; no proof or resolution is provided.