No no I don't think they're half sisters. Cleo comes from entirely different Marquis family. That Marquis family had an eldest son and a daughter from main wife and a illegitimate daughter from a maid. The legitimate daughter was set to be the empress, but she does mysteriously and the illegitimate daughter who was working as the legitimates daughter's maid, was made to go palace
Due to her origin, she could only remain as consort

So... from the chapters the empress and consort cleo are half-sisters then the first and second princes are both brothers and cousins? Interesting