Slot - "food" have not golden carrot

Isn't it on the brewing tab (slot) because it can be used for potions?

and this could be a duplicate of MC-1797

yes, but it can be in food and potions to!

1 item should only be able to exist in 1 tab (slot)

Golden carrots are not only food, but also used for brewing, which makes night vision potions.

1 item should only be able to exist in 1 tab (slot)

Unbreaking enchanted books beg to differ. Additionally, other brewing ingredients with different uses (spider eye, redstone dust) only appear in other tabs, and not in brewing.

Please see the note on MC-1797 - Unless the item was added after 1.16, this will not be changed.