A q-analogue of Sun's second binomial supercongruence

Let $n$ be a positive integer. Define the $q$-integer $[m]=(1-q^m)/(1-q)$, the $q$-shifted factorial $(a;q)_m=\prod_{j=0}^{m-1}(1-aq^j)$, and the $q$-binomial coefficient

$${M\brack N}_q=\begin{cases}\displaystyle\frac{(q;q)_M}{(q;q)_N(q;q)_{M-N}},&0\leq N\leq M,\\[5pt]0,&\text{otherwise.}\end{cases}$$

Let $\Phi_n(q)$ be the $n$th cyclotomic polynomial.

The q-Sun binomial conjecture. For every positive integer $n$,

$$\sum_{k=0}^{n}[3k+1]{2k\brack k}_q^3\frac{(-q;q)_n^4}{(-q;q)_k^4}q^{-\binom{k+1}{2}} \equiv0\pmod{(1+q^n)^2[2n+1]{2n\brack n}_q}.$$

The paper proves a related q-congruence with a different summand, while this proposed analogue is left unresolved in the supplied text.