There's 3 main parties to LK99.
L&K, are two PHDs taught by their now dead former professor. Their research into LK-99 is inherited from their former professor but they lacked funding, hence it was a hobby project for a long time, and they needed funding to work on it full time.
The Korean professor: A professor who started taking interest and sponsoring the project for the last few years. However, he likely didn't participate directly in the research much.
The American professor (Ethnically Korean): A professor who was brought in rather recently (Maybe last 1-2 years?), to help bring credibility to the team. He is probably the one with the expertise to perform measurement and ascertain that it is a superconductor.
The Korean professor got kicked out from the team for unknown reasons. This was evidenced in the April paper published in Korea, which lacked the Korean professor's name. Quantum center also removed him from the website.
4 months later, he was back with a vengeance, and published the paper, with only him, and L&K on it (ie, the 3 man paper). The Korean professor possesses no sample, and also lacks the original data for LK-99.
A day later, the american professor hastily rushed out another paper (The 6-man paper), with L&K, himself, and 3 irrelevant lab assistants.
Since the earlier Korean paper in April got 0 attention and was treated like a typical troll paper. They probably assumed posting on arxiv was just good material for later legal battles, but they could otherwise continue happily researching and patenting their material.
However, interest in LK-99 exploded like a nuke, because the first signal for credibility: That two professors were in a bitter battle over authorship, did not escape people's eyes.
2 days later, the Korean professor had a presentation at a Korean conference, but attendees were disappointed by his data and lack of samples (Prediction markets hit a low of 15% at this point).
However, the American professor took control of media communications, and quickly dissociated with the Korean professor, yet he completely stood by the claims of LK-99. Now the American professor has talked to numerous Korean media and directly sent an exclusive video to NYT.
Its interesting why L&K chose the American professor over the Korean one. Needless to say, if this works out, the interpersonal saga will end up in a Netflix documentary, and probably many court cases.
I should also note that the nobel prize is likely a secondary concern for the group. They aren't in a comfortable academic position where money is only a bonus. They were struggling PHDs for a long time. Nobel prize money is too little, and will come way too late to make a difference for their lives.
L&K and the American professor are likely trying to maximize the value of their patents and know how to sell to investors, rather than to make public verification ASAP, which would be optimizing for a nobel prize.