I see what you're saying but you're not really doing justice to the intent behind her actions. If she didn't search him out after the first time, they wouldn't have seen each other again. She instead set up a way for them to meet consistently without putting too much pressure on him via training, where they both more or less did their own thing. I'm not sure exactly how long that went on for but I'd wager at least a couple months. I'd say it's slightly idealized in that some people wouldn't forgive her at all but not really that bad.
Tbh I get that, but let's be realistic, her actions her creepy. She's normally a woman in her 20s (which is before she entered the FL body) it is incredibly CREEPY that she is swooning over a kid 10+ years younger than her. And not to even mention the acts that the former owner of the body inflicted on the boy. The intent of the author is to make her seem sweet and cheerful, but she's just plain obsessive and creepy. No matter how much you try to put it: she isn't giving him space (she should if she wants to make amends correctly), she's normally WAYYY older than the boy, and she just seems to loose every sense of wisdom.
If the age thing is a problem I suggest you stop reading these. Besides, she fell in love with him when he was an adult. She didn't get to choose what age she got reincarnated as. And she's not lusting after him, it's not really that different from looking at kid photos of your lover and going "aww that's cute". If she gave him space they'd literally never see each other again and Raon would end up dead, pick the lesser evil. She gave him about as much space as she could under the circumstances by choosing to train in the same spot instead of say, begging her parents to bring her over to his house, where he'd be forced to interact with her.
So there's a lot of back and forth between the group that dislike the female lead and the group that thinks she's cute and relatable. Now, besides the fact that the whole point of comment sections are so that people can give their feedback, thus whether the feedback is positive or negative it's a good thing for the author and translators (so long as the feedback isn't rude), I'm going to explain why I personally don't find the female lead that enjoyable.
Yes, she's "stanning" him super hard and fangirling at meeting her 2D love right now, and that's all fine and dandy, but one small part seems to have been forgotten and glossed over too quickly. She is not the original owner of this body.
What does this mean? Well the original owner of this body tortured Roan for years. Absolutely tortured. She hit him, picked on him, got others (even adults) to hit and pick on him, fed him POISON and was just general the worst kind of person short of killing him. In a sense, she was no better than his father and in the real world would get institutionalized or put in jail for the abuse she caused on the poor boy.
And then FL took over the body and tried to change things. Apologized for her actions, tried to be kind and fix the mistakes of the past. But she also just tramples all over his feelings constantly. She apologized, and basically immediately wanted to be best friends with him. She did mention at one point that she "doubted he would forgive her that quickly" but instead of giving him space and trying to prove her sincerity, she forced her feelings and emotions on him and made him have to deal with something new now.
Of course that worked out because there wouldn't be a story if it didn't, but IMO things resolved themselves too quickly. She said one phrase that made him happy, "I'll always be on your side" and that was all it took to get to his heart? And now he's starting to develop a crush on her, but just a year and a half ago she was still torturing him.
I am still reading this story because other than the beginning portion, I do enjoy the plot. Cliche as many areas of it are, it's still cute and I'm interested to see what they'll look like when they're older as well as how the author plans to play out the FL of the story that she jumped into and the harem of guys she had. But the current FL does seem kind of pushy and not exactly understanding of the situation she started in.
Just my two cents