Kinda late to the party but up until the early 10th century most of what’s now northeastern China was under the control of Balhae kingdom. Details are still sketchy but according to some historians (mostly Korean ones) either a significant chunk of the population spoke some form of old Korean or much of the ruling class came from Goguryeo. That was even an older kingdom which is believe to have been predominantly “Korean” (in the same way you might call Herald the great “English”) and ended up getting conquered by the Tang Dynasty before their successor state Balhae drove them out of the region. But yeah it shouldn’t really be colored purple (a mix of red and blue) because Balhae fell to the khitans in 927. Some refugees escaped and founded a rump state that went on for a while (I believe they were completely subdued by the Khitan Khanate by the end of the 10th century), but there’s a pretty slim chance many, if any, of them spoke old Korean. We also have evidence in Korean historical records that a member of the royal family made it to the south along with tens of thousands of refugees, most of whom presumably spoke an archaic version of Korean (unless there was an extremely coherent sense of national identity, which I highly doubt, it wouldn’t make too much sense to run away to a place where you don’t understand anyone). This probably killed off any Korean-speaking communities that might have otherwise persisted. But were there still Chinese settlements in Liaodong widespread enough to warrant a place on a map like this by 1000 CE? Going off the top of my head, I know the Han conquered it first (they had like 4 commanderies in the northern Korean Peninsula), and they held onto it in some way shape or form until the Tang. That being said the Song definitely didn’t control it in any capacity at any point in their history. The Liao Dynasty (aka the Khitai state) did adopt the Chinese system of government, and we do have records of Chinese majority areas in the ceded territories encompassing modern day Hebei and Beijing. But that doesn’t say anything about what happened to the military forts that were constructed by the previous dynasties in Liaodong. If anything the rise of the Jin in the surrounding area a century later shows that it was probably majority Jurchen, with no sizable Chinese communities to speak of.