For what it is worth, the Bard class is the most accurate class to describe reallife shamanists.
Maybe a Bard subclass can reuse the music abilities for various "pets".
Maybe call the subclass a "Mediator". The idea is, the Mediator is community leader who helps sort out conflicts between the members of the community. Notably, this community includes nature beings as well as Humanoids and other creatures of the community.
When the nature beings are helping the Mediator out, they are simply being neighborly. Like other members of the community, the nature beings appreciate the Mediator sorting out various problems, and are happy to do favors in return.
Charisma, including persuasion and negotiation, is an important aspect of the shamanist concept.