There's an inconsistency between "drinking" and "eating" animations, where the former work seamlessly both in the hotbar and the player's hand, whereas the later is only animated in the player's hand. I tried searching through differences between milk bucket + potions and food items - e. g. an apple - but they're all the same - they reference texture parents in the same way; so I found out that "eating" and "drinking" are found in separated .class files and "EatingAnimationClientMod" has a section regarding resource supports, which the DrinkingAnimationClientMod lacks. Oddly enough, it worked perfectly well back on Forge 1.20.1
I successfully fixed the standalone resource pack for 1.21.4 when it came out, but this mod simply doesn't work the way it's intended.