Sinca

It's not explained. Only in the sense that she chose the person for her, instead of it being fated.
I also found it strange at the beginning of the webtoon, her obsession with this little kid, but it eventually becomes background. I guess it's that whole kstory trope of 'they met as children, so they're meant to be'

That was exactly what the webtoon did. It's why it was so beloved.
Seems like drama writers have been giving into their worst instincts since getting their little paws on this story.
Changed the whole message and themes.

The drama has been leaning into all the clichés the webtoon avoided. It's a shame, really. The webtoon was quite refreshing for sidestepping those clichés.

I think you're right to be worried about A Good Day to be a Dog, because there's pictures of cha eunwoo filming the period scenes and he's dressed like a captain of the guards in joseon times, so it seems they've changed that part of the story.
No doubt because they were averse to the gender bending element ( which I thought was the most interesting part).
It's like here making Min Gi a more experienced character and more in the know and wiser than Ji Eum. Reeks of sexism.