Good story. Enjoyable read. The element of the protagonist's memories being wiped for each new world is an interesting premise, too. However, there are a couple of things to consider:
1. **Are Emotions Cringe?**
Our protagonist, Lin Dan, is a sociopath. She has a very low regard for others, a low regard for human life, and difficulty empathizing, and she rarely forms external attachments that she isn’t comfortable cutting off at a moment’s notice without hesitation. She also has a very analytical mind, can learn very quickly, and—most importantly—can act very well. While her mind is being wiped every world, it's important to remember she has thousands of years of subconscious experience.
Though she herself doesn’t seem to realize it, her motivations always align exactly with whatever the last wishes of the previous host were—but she has very little reason to care about any of these people (which we see in how she acts) and in all other aspects is a generally uncaring person. Suspicious.... I hope the overarching plot addresses this.
2. **Requiem for an OGFL**
The "OGFL" character for each arc is less and less antagonistic or deserving of the punishments they receive. If you put yourself in her shoes, knowing what she knows and the previous actions of that arc’s pre-transmigration Lin Dan, there isn’t very much that a normal or even moral person would do differently. She generally acts with genuine honor and doesn’t cheat even when she has the opportunity to. She also seems to have some sort of "mental compulsion" to act in opposition to Lin Dan—it’s described as a sudden inner force so strong it almost forces her to move. All the most antagonistic moves made against Lin Dan are made by people around her orbit, generally acting without her knowledge. From the bits we get from her perspective, it seems like her moral compass fluctuates between "benign self-interest" (wants to better her lot in life as long as it doesn’t hurt others—also known as a normal person) at the lowest and "genuine desire to work towards the greater good."
The only outlier is the military arc, where she schemes a little bit. What she does is by no means altruistic, but if you step back, the goals of her plot are: don’t marry the man she doesn’t like, give that man to her sister who (as far as she knows) has a massive crush on him, and marry upwards. The one time she draws someone else into the scheme other than Lin Dan, it’s an accident she couldn’t have predicted. I don’t know about you, but I wish I had an enemy like that! In the dropped timeline of that arc, the man treats her sister awfully and doesn’t give them a chance—but that’s not the OGFL’s fault. As far as she knows, he’s a sweet guy. Later in that timeline, she reports on his secret plans to her husband. I don’t know if I’d blame her for that. If your husband’s enemy keeps coming around to tell you all his deepest secrets and battle plans, I think it’s pretty obvious you’d share that info with the husband. She wasn’t sleeping with him or anything. This later causes disaster to the nation, but again, how could she know? In the end, she falls short and ruins herself because she just isn’t as good as Lin Dan. She tries her best, but she can’t quite measure up to the millennia-old genius sociopath that follows her from life to life—someone who surpasses her in whatever she thinks she’s best at in that life when she’s at her peak, before crushing her. Her memory is wiped so she never learns, and she’s compelled to set herself against this demon whenever they meet. Like, this is the villain? This sounds like an ironic torment you’d get from an evil genie or something.
In the end, we root for Lin Dan because she’s fun, and she’s the protagonist of the story. That’s fine if that’s what you want to write, but it’s kind of ironic that a story (and genre) built around subverting the roles of hero and villain being assigned by fate would literally be doing the exact same thing.
Also, the Chinese Medicine stuff in the doctor arc was kind of weird. All those author’s notes complaining about Western medicine existing were kind of funny. Like, I don’t think that the author is complimenting traditional medicine like they think they are when the first step of the treatment is to "circulate your qi." Last I checked, most doctors can’t do that... I’ll stick with Western medicine till then.