The second q-analogue of Liu's Dwork congruence

Let $m$ and $n$ be positive integers with $n\equiv1\;\allowbreak(\operatorname{mod}4)$ and $n>1$, and let $(a;q)_k$ denote the $q$-shifted factorial. The q-analogue conjecture.

$$\sum_{k=0}^{mn-1}\frac{(1+q^{4k+1})(q^2;q^4)_k^3}{(1+q)(q^4;q^4)_k^3}q^k \equiv \frac{[n]_{q^2}(q^3;q^4)_{(n-1)/2}}{(q^5;q^4)_{(n-1)/2}}q^{(1-n)/2}\sum_{k=0}^{m-1}\frac{(\frac12)_k^3}{k!^3}\;\allowbreak(\operatorname{mod}\Phi_n(q)^2).$$

This is presented as a different q-analogue of the first case of Liu's supercongruence and as a refinement of an earlier congruence.