Commutator length of powers in free products of groups

Abstract

Given groups $A$ and $B$ , what is the minimal commutator length of the 2020th (for instance) power of an element $g\in A*B$ not conjugate to elements of the free factors? The exhaustive answer to this question is still unknown, but we can give an almost answer: this minimum is one of two numbers (simply depending on $A$ and $B$ ). Other similar problems are also considered.