What does "the hard edge of" mean

It means nothing; it is merely excess verbiage by a bad writer.

"Hard" here means something like "blunt, agressive". It's like the phrases "hard power" and "soft power" where soft power is influence based on size, position and political influence and hard power is militarily based.

Hey Jinmin,how gozit?

"the hard edge of its rising power" means the strongest, toughest, most to be feared part of its rising power.

its alludes to a sword

might, strength, cutting

let the ascription of materiality to an abstract noun henceforth be known as a jinmin in your honour