The IPA for 不 in 2021 Mandarin is pʷu4, and in 2021 Cantonese is /pɐt5. These don't sound like *An.
From what did An phonologically change?
Can you please expound the steps of 不's phonological change?
I quote 不知 - Wiktionary.
Etymology
The basic negating root of the Old Korean negatives is disputed. Because all conventional reconstructions begin with *ant-, many South Korean linguists, including Lee Seung-jae, have proposed that the base form was *anto-, producing 不冬 (*ANtol), 不只 (*ANTOk), and (via deletion of the minimal vowel ) 不知 (*ANti). Other scholars, including both Koreans and Alexander Vovin, have argued that the negative root is *an and that *tol, *tok, and *ti are as of yet poorly understood suffixes. Vovin notes that likely borrowings in Tungusic appear to suggest that the root was *an-. In the case of 不知, the orthographic variation, perhaps reflecting dialectal differences, may also be suggestive of an originally *an- root.
This was probably borrowed at some very ancient period into Proto-Northern Tungusic as *anti, producing forms such as Udege language anči and Even language āt.