Does the pendulous flesh at the beginning of the throat, which water reaches during gargling, count as part of the throat such that water reaching it during fasting would affect the validity of the fast, given that gargling is disliked but does not break the fast?

The fast is broken by water reaching the throat intentionally. However, if it reaches unintentionally, such as during rinsing the mouth (madmadah) and sniffing water up the nose (istinshaq), the fast is not broken, even if one exaggerates in them, because its unintentional reaching the throat is like dust. The uvula is not part of the throat but overlooks it, and it is considered part of the outer mouth. Gargling is disliked for a fasting person unless there is a need, and one must be careful not to swallow anything from it.