Tauraso's $q$-supercongruence conjecture for central $q$-binomial coefficients

Let $n$ be a positive odd integer. Define the $q$-Pochhammer symbol by $(a;q)_k=\prod_{j=0}^{k-1}(1-aq^j)$, and let ${2k\brack k}$ denote the $q$-binomial coefficient.

Tauraso's conjecture.

$$\sum_{k=0}^{n-1}\frac{q^k}{(-q;q)_{k}}{2k\brack k}\equiv (-1)^{(n-1)/2}q^{(n^2-1)/4} \pmod{\Phi_n(q)^2}.$$

This strengthens the previously known congruence modulo $\Phi_n(q)$ and is a natural generalization of Tauraso's conjecture for odd prime $n$. The source does not provide evidence that the assertion has been resolved.