It really depends on the specific plot and character development in the manhwa. Sometimes it happens early on, and in other cases, it might take a while.
It's a complex tale of a female character who finds herself in a challenging relationship with a tyrant. There are lots of twists and turns along the way.
It could be Voldemort. If this story is set during the time when Voldemort was still a threat, he might be trying to stop Harry from getting home. Maybe he has a plan that involves keeping Harry away from the safety of his home so that he can be more easily attacked or manipulated.
Well, perhaps Harry misses the warmth and safety of the Burrow. He might be on some dangerous adventure away from home and his longing for home gives him the motivation to quickly finish whatever task he's on and return. For example, if he's in a dark forest full of unknown creatures while searching for a powerful magical item for the Order of Phoenix, he'd constantly think about going back to his simple but loving home environment.
To be a successful villainess in a manhwa, you need to have a strong personality and a clear goal. Also, a unique style and the ability to outsmart others are important.