> The modern Korean writing system (hangul) is unrelated to Chinese.

This is true, though newspapers and some other written texts make use of mixed hanja-hangul script (hanja honyong) where Chinese characters (Hanja) are interspersed with Hangul in the same piece of Korean text in order to disambiguate homonyms.

Interestingly, you could argue this is attempting to solving the flip-side of the problem that Furigana in Japanese solve (where a reader may know the phonetic reading of a word but not the Kanji that are used to write it -- though native-level Japanese speakers don't need Furigana to read the vast majority of text since Kanji represent more conceptual information than Kana).

The Mongolian Cyrillic one is quite a trip. As a native Russian speaker, it just looks so odd. Like a broken website encoding from early days of the internet.

That's not completely true. Hangul characters are based off of Chinese characters.

Hangul is a syllibary where each character is formed from a consonant and a vowel symbol being merged in a consistent way. Even if a few of those symbol fragments are similar to chineese, the structural differences are stark enough that calling the whole thing based on chineese is misleading and deceptive.