The emperor’s power didn’t matter as much as his central importance in their religion. He was like a god, and the Postdam Declaration didn’t make it clear that the emperor would be safe. Hence why it was rejected.

https://homework.study.com/explanation/why-did-japan-reject-...

I may have misremembered reading about this years ago. I don’t think the terms changed, but there’s an argument that if the US was more clear about the emperor’s position post-surrender, the Japanese would have surrendered much sooner.