The cloak is a prominent feature of Prospera's costume. What does this cloak add to her characterization? Is it consistent with the descriptions in the text?

In this adaptation of "The Tempest", Prospera is a magician by profession. She is accused of practicing witchcraft. The cloak is a prominent feature of Prospera's costume and this suits the attire she dons for her role as a magician.

Yes, it is totally consistent with the text as the text mentions that Prospera has some specific controlling powers over nature and specifically animals.