I really wish I had the relevant literature at hand to do a larger overview of post-Japanese decolonization, but unfortunately those books are at my parents' house and I can't get at them due to coronavirus.
Instead, I'm going to focus on one specific area that just so happens to be the one most affected by Japanese imperialism: namely, the Korean peninsula. The decolonization of Korea, and later the Koreas, is a long and messy affair that some argue is still incomplete to this day, and it's hard to do it justice via Reddit post, but I'll do my best.
The decolonization effort in what is now South Korea had a lot of fits and starts. As the Japanese retreated from the peninsula, a number of local councils known as People's Committees sprang up behind them in order to fill the resulting power vacuum. Consisting mainly of community leaders, the Committees functioned purely on an ad hoc basis with no single unified agenda. Their goals largely centered on maintaining order and protecting food supplies, but some extended their efforts into removing Japanese collaborators from positions of authority and redistributing their land to small tenant farmers.
The largest of these was the Committee for the Preparation of Korean Independence, headquartered in Seoul and led by former Joongang Ilbo (English: Central Times) president Yeo Un-hyung. The CPKI was large enough that it aspired to become Korea's post-colonial government, and started meeting with other People's Committees throughout the peninsula to try and make this a reality. It worked, and in the interim between the announcement of Japan's surrender and the signing of the treaty between Japan and the Allies, the CPKI announced itself as the provisional government of Korea. A week later, on September 6th, 1945, they proclaimed the new Korean People's Republic.
The formation of the KPR was met with consternation by the arriving American troops. They suspected the KPR of having Soviet ties, and they most definitely didn't trust Yeo, given that he was a former Communist who had once ventured to the USSR and personally met Lenin and Trotsky. John Hodge, the commander of the American occupying forces, argued that the KPR was "a Communist regime set up before our arrival," and refused to recognize it, preferring to instead work with the Korean Democratic Party, a rival organization that was largely conservative and contained more than a few people who had collaborated with Japan during the colonial period.
Over the next three years, the U.S. Military Government in Korea (USAMGIK) essentially rebuilt the colonial-era bureaucracy, using the existing administrative machinery of the Japanese Government General to consolidate control over the southern half of the peninsula. The changes they made to the Japanese structure were purely cosmetic, and the upper echelons of the bureaucracy were staffed with KDP members. While the USAMGIK recognized that they wouldn't be able to exercise direct control over Korea forever and would eventually turn things over to Syngman Rhee in 1948, the damage to the Korean decolonization project had been done. South Korea would continue to be mostly governed via Japanese-created institutions until the overthrow of Rhee's government in 1960. The interim government that replaced it was short lived, and South Korea fell to military dictatorship - headed, not coincidentally, by men who had been trained at the Imperial Japanese Military Academy.
Japan would continue to cast a long shadow over South Korea during military rule. Park Chung-Hee, the dictator who dominated the country from 1961 to his assassination in 1979, drew heavily on the Meiji Restoration as he sought to transform South Korea from a largely pre-industrial society. The institutions he created to carry out his economic reforms - the Economic Planning Board, the Ministry of Trade and Industry, and the Ministry of Finance - all took heavy inspiration from their Japanese antecedents, and Park made the Meiji-era mantra of “rich country, strong army” the motto of his project. Even the Yushin constitution, a 1972 governmental reboot which granted Park near-absolute power, is named after the same Chinese root word as “meiji.”
TL;DR - the machinery of Japanese rule in Korea stayed in place well after the end of the empire, and the influence of Japanese institutions would stick around for decades after.
Of course, all this is to say nothing of the legacy of the United States in South Korea, which looms just as large as Japan’s. In some ways, South Korea never fully decolonized, but merely traded one occupier for another.
I will talk about the North in another post, and expand upon some of the points raised here later. Writing something like this in one sitting is a test of endurance, and I'm out of gas for the moment.
Sources:
Brazinsky, Gregg. Nation Building in South Korea: Koreans, Americans, and the Makings of a Democracy. (Chapel Hill, NC: University of North Carolina Press, 2007)
Choi, Youngho, Lee, Peter, and de Bary, Theodore, Eds. Sources of Korean Tradition, Vol. II. (New York: Columbia University Press, 2001)
Cumings, Bruce. Korea's Place in the Sun. (New York: W.W. Norton & Co., 1997)