There are some English sources on it such as the Wikipedia page on Korean People's Association in Manchuria, and some anarchist literature such as The Story of the Korean Anarchists and the Anarchist Revolution in Manchuria, 1929–1931 or The Korean Anarchist Movement. But a major study on Korean anarchism Dongyoun Hwang (2016) Anarchism in Korea doesn't mention it all! It mentions Manchuria in passing, but that's it.
So did an anarchist commune really exist in the Shinmin region in Manchuria during 1929–1931? If so, what are reputable sources for reading up on it?
My, that's a rosy picture!
The Korean People's Association in Manchuria (KPAM) was more the territory of Kim Chwa-chin. (It was also called the Korean People's Autonomous Zone and a bunch of other names. I'm sticking with KPAM purely for convenience.) Kim Chwa-chin is a fascinating figure in his own right. He was born the son of an important nobleman, married the daughter of a prominent noble family, and went on to have a military career before becoming a mob boss and eventually a revolutionary. He managed to straddle the line between the Nationalist and Communist resistances to Japan. Both North Korea and South Korea have statues of him. His hometown (in the South) has a museum and the North includes him in museums of revolutionary heroes.
Kim was invited to the Soviet Union along with other prominent Korean Communists in 1920. He refused, instead remaining in Manchuria to fight directly. Kim was one of the best generals the Korean revolutionaries had. He set himself up as a minor warlord in the Chinese civil war, operating mostly in parts of Manchuria with a large Korean population. He also used his mob connections to make money to fund his army and acquire weapons. Kim had gained control of most of Shinmin by 1925, partly because of local politics involving Zhang Zuolin.
Shinmin remained under his forces control from 1925 to 1931. Kim implemented various Communist and anarchist policies and proclaimed the KPAM in 1929. But the reality was that Kim retained control of the military. He, and a clique of officers, retained real power. Kim was both the supreme commander and the chairman of the region. The KPAM was mostly a way to create limited self-governance under the framework of Kim's rule. When Kim was assassinated, his subordinate officers immediately began to fight each other for control. Under pressure from other forces, many of them simply abandoned the region. By 1931 the KPAM had been eliminated.
Kim's family fled back to Korea, where they went back into the revolutionary/mob business. His son, Kim Du-han, led a gang in Seoul and ultimately sided with the Korean nationalists. He became an important politician in South Korea. His daughter (Kim Chwa-chin's granddaughter) is a mid-level Korean politician, important in one of the smaller parties.
If you want to read up on it, read up on Kim Chwa-chin. It wasn't so much an independent state or a revolutionary uprising as Kim imposing his ideology on a region he conquered. The biography put out by Hanseong is a pretty good overview. There are other biographies floating around too. You can also read up on Korean revolutionary history, he pops up a lot in the 1920s. And, in a less historical sense, The Age of Wild Men is a Korean drama that follows the life of his son, including their time in the KPAM. He's something of a cultural figure and that's not the only work that features him, just the most famous.
PS: Despite the name, Kim had no family relation to the Kims that now rule North Korea. Kim is an extremely common Korean surname. He did know Kim Il-sung personally, though.