What is the basic rhythmic movement of capoeira that has a dance-like quality shifting weight from one foot to the other while maintaining balance and mobility?

Ginga.

Explanation:

Ginga is a dance style that evolved from the capoeira dance style. Capoeira dance form originated from Brazil.

Ginga is the basic rhythmic footwork of swinging or rocking back or forth on legs in capoeira.

Capoeira is an Afro-Brazilian martial art which is combined with the elements of dance, music, and acrobats. In this martial art form, Ginga is used as a technique.

So, the correct answer is Ginga.