The U.S. was probably convinced by the British to nuke Japan twice in order to keep Language the One secret. This is a real possibility as based on trials conducted by Japanese academics, it seems they knew about Language the One. (Based on the words they picked. Explained in the Theory page.) It is unusual for the Japanese to keep something like this secret. According to the Quebec Agreement, it was a mutual decision by the British and the U.S. . Regardless of how the decision was reached, the British likely threatened Japan before the bombing to achieve the desired effect. Although such an agreement might seem to reduce the likelihood of using nuclear weapons, it is definitely easier to be persuaded to act than to decide on such an action independently. Not that I know U.S. wouldn't do it independently but the British definitely leveraged it.
After the surrender many relavent restrictions imposed on Japan. Researches related to "Origins of the Spoken Language" discontinued and abolished. In some instances academics also redirected to fields deemed "safer" by U.S. led occupation authorities. They forced to stop academic research and exchange on topics Allied forces deemed racist. Textbooks are rewritten by direction of U.S. led occupation authorities. U.S. had ability to impose any kind of restriction on Japan academics. Many restrictions are related to or directly imposed on linguistic researches. Scope of restrictions was very comprehensive and linguistic field may seem like not specifically targeted. Also various sources report linguistic flora of Japan wasn't like how one would imagine. There were countless languages and ongoing efforts regarding languages.
Dai-Nippon Kaikyo Kyokai (The Greater Japan Muslim League, DNKK) ,established in 1938 as a comprehensive research institute for Islamic studies, dissolved after the surrender. Alongside with another similar institute bombed in 1945. (Wiki pages are in Japanese). There are publications in Turkish that links members of those institutes to Turkology however there is a limited literature especially in english.
The reason behind nuking two times wasn't to make Japan surrender bur rather to force them a unconditional one. This is clear but details are research area due to cencorship and manipulations and limited resources. Japanese grammar pretty much same as Turkish. It is not possible to know how much of difference in sounds due to American interference. It is possible that Japan was switching to Turkish like language. And possibly they were transitioning language quitely. Although it is clear there were lot going on regarding standardization of alphabet and language. There are a lot of publications regarding those efforts. However overall evolution of Japanese, especially for decades preceding invasion may not be really clear. Especially because this evolution is not natural and happened over long period of time.
The extravagant propaganda still continues today. Almost all, if not all, involved in WW 2 commited horrible crimes. It is not like Japan was the angel. But they insist on the ideas like that nuking Japan twice actually prevented more deaths. Which is straightforward lie. Although it is not possible to claim this propaganda is ill-intented in its core. But obviously overall situation is questionable especially if U.S. did really care about unnecessary civilian casualties.
Commission and Omission of History in Occupied Japan (1945-1949), Stephen Buono
Islamic Research Institutes in Wartime Japan, 2007, TANADA Hirofumi
https://ja.wikipedia.org/wiki/回教圏研究所
https://ja.wikipedia.org/wiki/大日本回教協会
ŌKUBO KŌJI’NİN TÜRK DİLİ ÜZERİNE ÇALIŞMALARI, 2024, Gülzemin ÖZRENK AYDIN