Imo they just seem to be showing a good platonic/familial relationship - good friends, cousins, siblings, those vibes. Nothing more.
I can understand where your fear may be coming from due to how many step-sibling romances there are in historical rofan manhwas (it's not a lot in the grand scheme of things, but enough to make one worry for it to happen again), or how they tend to make all close male-female relationships romantic at some point. I admit I had the same fear, although I was feeling confident they wouldn't do that considering how closely related they are and how the King mentioned that early on.
For those who have read the novel, please, please, please tell me the ml isn't here nephew, please. The story seems to be going great and I don't wanna drop it at all.