I'm in France, so my answer might not apply to where you live, but we typically have yearly festivals, monthly open mics in theaters, plus the occasional one-shot in theaters (where a famous storyteller is invited for his new/famous set of stories).

We are considered as actors/comedian and are paid accordingly (or not at all, for open mics, obviously).

My experience with oral storytelling has been through festivals dedicated to it. This[1] is a list of storytelling festivals around the US and some other countries.

[1] http://www.sostoryfest.com/festivals.html

The Moth, maybe?

https://themoth.org/about-moth-events

A local group does oral storytelling, and it is promoted as such.

https://kingsplayhouse.com/event/the-four-tellers-the-last-l...