Well MC tells her, that she is to move on when he leaves for his world.
And the pregnancy is kinda eye raising, but remember it's not even MCs child, he's in Aaang's body, therefor it's Aang's child and Aang is the one Katara canonically marries anyway. (Also the pregnancy stuff is only in game because a player may be into preggo stuff - therefor it matters even if it doesn't storywise
).
All of this could be addressed but it doesn't really have to. From Katara's perspective the MC is the essence of some otherworldly being on a mission from the gods, who temporarily inhabitated the body of the Avatar Aang, a guy she was interested in to begin with and than left to return at a later date in another body. I have no problem with her moving on in any way.
But aside from me being able to hand wave this away and regardless of whether you agree with me or find this very distracting or something in between - it's still a result of Mity's writing choices, and not a result of having some weird story elements imposed on him that would arise without the MC. So that's something I guess.