A further q-supercongruence for the 2k central-factorial sum

Let $p,m,r$ satisfy the hypotheses of the source's Theorem 2k2k2k-1. Further q-supercongruence conjecture.

$$\sum_{k=0}^{p-1}\frac{(q^m;q^m)_{2k}(q^r;q^m)_k(q^{m-r};q^m)_kq^{mk}}{(q^m;q^m)_k^4(-q^m;q^m)_k^2}\equiv0\pmod{[p]^2}.$$

The supplied text contains only the cross-reference to the theorem's hypotheses and no evidence of resolution.