I don't know what the creators' intentions were regarding the favicon. It is, however, the katakana "chi" (チ), which corresponds to the name "Chicory". Seems bizarre, but that's the connection I saw.

Katakata, like zhuyin, is "hanzi/kanji written small", just as hiragana is "hanzi written quickly". I see hanzi/kanji, katakana, and zhuyin (but not hiragana) as all part of the same "alphabet" used to build up hanzi recursively. Many katakana are components of hanzi.

Maybe, but this is rather like using a Cyrillic letter in a Spanish-teaching website. "What language are you teaching anyways?"