I wonder who is princess bari

She's the mother of all shamans. If u know shamanism in Korea follows a strict matrilineal line and woman dominated for he most part. Princess Bari origin has a lot of variations but what stays consistent is she displayed exemplery filial piety towards her father (I forgot detail lore) n hence she's hailed as the first ever shaman or patron diety of all shaman women in Korea. She has power of exorcism, guiding one to underworld and over birth and fertility

Thanks a lot for this. It's very interesting

Although many variations, core points: she was born as the 7th daughter of a king and he discarded her due to his disappointment->as always he wanted a son. Then she was raised either by a deity or some good ppl who kinda became her parents.
When she learnt about her abandonment she didn't hold a grudge though and when her father became sick only she decided (either the king ordered her to, or she was informened ab his situation) to go to the underworld for the water of life, which can cure everything.
There she went through some trials, didn't waver or doubt. Cured his father and became a deity herself. In one version I read one of the "cosmic law" was that she can't meet her family ever again.