By the general rules of $(n,r)$-categories, a $(2,1)$-category is an $\infty$-category such that

any $j$-morphism is an equivalence, for $j \gt 1$;

any two parallel $j$-morphisms are equivalent, for $j \gt 2$.

You can start from any notion of $\infty$-category, strict or weak; up to equivalence, the result can always be understood as a locally groupoidal$2$-category.