So Haewon is a distant relative of the brother (?) of the emperor. They are probably related through his maternal side, considering Haewon is not royalty.
Also confirming that distant relatives does not mean incest. They are related but far removed enough for it to be "safe" biologically. I bet by branch family it probably has hundreds of years of separation, family-wise.
Also he's so cute, definitely too pure of a cinnamon roll uwu