>>2498805Major spoilers ahead.
I interpreted the other world as another world or dimension. Mato can see into the other world sometimes when she sleeps and dreams, but she is unaware that another world exists so until she goes there she cannot really make sense of it. Saya and Yuu know of the other world and can interact with their other selves to an extent, but how they became aware of the other world isn't entirely clear. Their awareness seems to surface when Yuu switches places with Strength, but I cannot really see how Yuu was special and was aware of the other world while others were not, other than the fact that her suffering is much greater than the others. Other than that the people in both worlds seem mostly unaware of each other.
I believe that there are other people who have other selves, Strength was talking about how she fought many of them before BRS defeated her for the first time, she also said that BRS defeated many of them. I have no way of knowing for sure, but I suspect that Black Gold Saw has a similar battle record; I suspect this because Saya seems to be some kind of "hunter", who purposefully makes people feel upset and then kills their other self with BGS. This last statement definitely has holes in it so I only call it a hypothesis.
Also, I can't help but think that this song would fit Insane BRS perfectly, especially during her introduction and battle with Black Gold Saw.
https://www.youtube.com/watch?v=ZXVoNsHgYQ0 