Korea was under direct Japanese rule from 1910 to 1945. Within this 35-year period, the period you are thinking of when Japan attempted to crush Korean culture only lasted from 1936 to 1945, and I think it is generally considered part of wartime fascist culture. Perhaps if Japan had maintained control over Korea after the war, a continued assimilation program would have been seen as cultural genocide.

When Japan annexed Korea in 1910, it banned public gatherings and newspapers, in order to prevent unrest (Korean-language magazines were still permitted). Naturally Koreans were seething over this authoritarianism and its enactment in everyday colonial violence, and they gathered in Buddhist, Christian, and Cheondogyo religious institutions, the only exemptions to the ban, in order to plan a nationwide general strike that would appeal to global civil society and the great powers. This culminated in the March 1st Movement of 1919, when millions peacefully went out in the streets. Religious leaders and activists released a Korean Declaration of Independence. Japanese police arrested and beat as many people as they could, a response which the activists had anticipated.

Japan’s response to this was to reorient their colonial system. They recognized that the authoritarian stance they had taken appeared illegitimate to Koreans and to the world (Christian missionaries were especially appalled by March 1st). From 1918 to 1936, there was a period called “cultural rule” when hangul was taught in schools, and independent Korean-language films and cultural products were promoted, such as the 1926 pro-independence film Arirang. In 1930, Koreans were allowed to fill out election ballots in hangul. There was a surprising amount of acceptance of this system from Korean leaders, even though the system remained strictly colonial, with Koreans never being granted the full range of civil rights allowed to Japanese people. This is part of the phenomenon of mimicry found in many colonial situations, with colonized peoples becoming willing to take extreme steps because full equality seems right around the corner.

Cultural assimilation, or naisen ittai 内鮮一体, began in 1936, with the obvious context that Japan had now invaded Northeast China and Korea had become an object of military strategy. Korean classes in schools were gradually cut down and Japanese education intensified. Even at this time, in 1938, the Japanese Governor-General of Korea issued the first ever order to protect Korean cultural treasures. For ultranationalists in Japan, Korean culture was considered to have ancient unity with Japanese culture, so Korean treasures were worth protecting. But on the other hand, this was the era when Korean schoolkids were made to bow at Shinto shrines [edit: also, pressuring Koreans to adopt Japanese names (sōshi-kaimei), distributing intensely whitewashed textbooks, attempting to convert political dissidents through police custody sessions called tenkō as well as propaganda,] etc., all in the name of unifying the two cultures. From 1943, Koreans were conscripted into the Japanese army, where they were treated especially brutally.

Many Korean treasures, for example the 1500-year-old Yongmyong Temple and every known print of the Arirang film, were actually destroyed during the Korean War, due to widespread use of destructive and murderous weapons like napalm on the American side. However, in the post-Korean War period, South Korea was ruled by a dictatorship which regularly tortured and killed dissidents, and it was dangerous to talk negatively about the continued American presence. Hence, the rhetoric often vaguely suggested that Japan had robbed Korea, which is after all true from an economic standpoint.

(edit: Removed statement about deforestation as it was questioned in replies, and I can't find the source where I read it to accurately quantify it. For more info on colonial forestry, please see Seeds of control: Japan's empire of forestry in colonial Korea [2020], which is a much more solid book than how I tried to summarize it)