I'm not an expert in Korean, nor do I speak it. However, a cursory search of the internet reveals that Koreans still use Chinese characters in the field of law, for clan names which are still traditionally written in Chinese characters, and in other historical contexts.
Korean was originally written with Chinese characters before the 15th century when Hangul was invented. So if you need to study/read/quote old texts that aren't in modern Hangul, you may need Chinese characters.
After doing a little more research on the fonts, it appears that the language variant of each font contains all the characters used by the other languages, and the Noto CJK help page says the following:
Noto Sans CJK and Noto Serif CJK comprehensively cover Simplified Chinese, Traditional Chinese, Japanese, and Korean in a unified font family. This includes the full coverage of CJK Ideographs with variation support for 4 regions, Kangxi radicals, Japanese Kana, Korean Hangul, and other CJK symbols and letters in the Basic Multilingual Plane of Unicode. It also provides limited coverage of CJK Ideographs in Plane 2 of Unicode as necessary to support standards from China and Japan.
And further down the page.
Language-specific OpenType/CFF (OTF)
Each font sets one language as the default. Note that each language-specific font does support all four languages and includes the complete set of glyphs. However, you need an application program that can invoke an OpenType locl GSUB feature (e.g. Adobe InDesign) to access language-specific variants other than the default language.
There's a lot more information on the help page, probably best to refer to that for a full explanation.