Foreigners residing in South Korea can work at domestic companies and organizations only with work visa including residence visa which has no activity restriction.
How about working in Korea after getting a job from companies and organizations abroad which have no Korean branches? For example, if you get a job from German IT company, do you need still long term work visa? Don't you think it is not required since that job has no relation to Korea?
Korean authorities confirmed work visa type is required even in this situation.
By the way, nomad visa may be available soon in Korea. This visa holders can work remotely in Korea for about 1 year. *Workation visa will be issued from January 1, 2024. (F-1-D)