The trivial group gives ordinary 2Vect

Since $G$ has one element, every tuple in $G^4$ is $(e,e,e,e)$. Normalization forces $\omega (e,e,e,e)=1$, so the convolution grading has one summand and the pentagonator is the identity. Thus the underlying monoidal 2-category is the usual 2-category of finite semisimple $\mathbb{C}$-linear categories, linear functors, and natural transformations with Deligne tensor product.

The simple-object list in [F2] becomes the singleton $\{{\delta }_e\}$, which is also the monoidal unit. A finite semisimple category with $n$ simple labels is the direct sum of $n$ copies of ${\mathrm{V}\mathrm{e}\mathrm{c}\mathrm{t}}_{\mathbb{C}}$, so this is exactly the ordinary 2-vector-space example and its unique simple-object class.