Really? I knew a lot of things had been hinted at but I didn't know that Earth, Empire, and Kohaku being a heavenly king had all been confirmed. All I remembered for sure was that the Will of the World was confirmed to be a thing and that Kohaku knew what it is. Do you remember where those other things got confirmed?
Can't remember each chapter, but I can say that it isn't like it was blatantly said, but the hints are too strong to be anything else.
Kohaku has all the little motifs of being the white heavenly king, and she is too strong to just be a random person, especially with some of the techniques she uses (like the wood magic she used against that castle, and that a friend of her's was the one that created it).
This being just another continent in the same world as Helck is pretty much clear by the way some things are said, Kohaku is here, and it was confirmed in Helck that the world where they live is Earth thousands of years in the future, like tens of thousands by what was hinted, maybe close to the hundreds.
Oh... little thing it just came to my mind... the moss "birds" race that Piyui belongs, they are a confirmation that this is the same world, can't believe I was leaving that out of my mind XD.
And the mysterious guy that appeared a few chapters back may be Kenros' dad, who was confirmed to be a high-ranking subordinate of the white heavenly king and is searching for his liege, that is... Kohaku.
See a lot of little details.