M2 brane $S^3/\mathbb Z_k$ instanton partition function in ${\rm AdS}_4\times S^7/\mathbb Z_k$: 2-loop correction

As was shown in arXiv:2609.14497, the 2-loop correction to the partition function of M2 brane wrapping $\mathrm{AdS}_2\times S^1$ inside $\mathrm{AdS}_4\times S^7/\mathbb{Z}_k$ vanishes, in agreement with the localization prediction for $\frac{1}{2}$-BPS Wilson loop in ABJM theory in the grand-canon