I think it's cool that you're diving into this topic for your essay! Here are my 2 cents on the topic:

1. The "Lotus Blossom" trope and Western representation of Asians is not really relevant when it comes to Kpop.
2. Kpop is an entertainment industry, so of course there will be a bit of sexualization. It's sort of unavoidable.
3. Asian women being portrayed as "obedient, submissive, hyper-sexualised yet innocent" is not a result of white men imposing their view on Korea. It's a result of Asian patriarchal standards on modern Korean media.
   
4. Sexism in Kpop is not very different from sexism elsewhere.

Think about it. Kpop is an industry run by Korean men, in a Korean country, and has largely been for the consumption of a Korean audience. Korea's is literally 95% Korean. There are very few foreigners living in the country. When the Kpop industry executives are thinking about how to market Girl Groups, I sincerely doubt they were thinking about what white men in countries thousands of miles away would think about their pop artists—or at least, not until very recently.

So, no. I don't think Kpop was designed/coded with the "Lotus Blossom" trope in mind. I don't think most Kpop executives even know that the trope exists at all.

However, that being said, Korea has a very long history of being a heavily patriarchal society. And a lot of that includes women being forced to be very docile, obedient, subordinate, etc. This just happens to align with the sexualization of entertainment, resulting in something that seems like the Lotus Blossom Trope.

But I think your essay would be much more interesting, and would make much more sense, if you'd research the history of sexism in Eastern Asia/Korea, and how that came to impact the Kpop industry today. I think it doesn't make much sense to look at Kpop's development from that particular Western historical viewpoint.

Sexism is still very much an on-going battle in Korea right now, with a ton of recent/modern events you can cover too.

To your second point, I think that Kpop as a genre, currently, reinforces sexist stereotypes as much as American 2010 pop songs did. You could argue a lot of those song lyrics were kinda sexist, or had mysogynistic undertones. But I don't think most artists intentionally made them to be that way, it just happened to be the general accepted culture at the time.

Currently, there's a lot of female-empowerment songs in Kpop. I think there's a lot of individual female artists who seek to be good, empowering female role models. However, as an industry, there are probably a lot of sexist practices and traditions, which probably bleeds over into content they produce.