追加 and 補充: adding something and replenishing a supply
Compare adding a menu item with replenishing paper, including situations where replenishment still leaves too little for the next day.
Adding to what already exists
追加, read ついか, means adding to something existing. メニューに新しい料理を追加しました。 means that a new dish was added to the menu.
参加者が増えたので、椅子を追加しました。 says that chairs were added because the number of participants increased. It does not say the earlier chairs were broken.
Filling a shortage or depleted amount
補充, read ほじゅう, means replenishing a shortage or reduced amount. プリンターの用紙を補充しました。 says that the printer paper was replenished.
棚の商品が少なくなったので、補充しました。 says that shelf stock was replenished because it had become low. Identify from context what had been depleted.
Overlapping actions and whether the amount is enough
Adding chairs to fill a shortage can be viewed through both 追加 and 補充. Distinguish the focus on adding from the focus on filling a gap.
用紙を補充しましたが、明日の分には足りません。 says that paper was replenished, but there is not enough for tomorrow. Replenishment alone does not establish a sufficient total.
Does メニューに料理を追加しました。 mean that depleted dishes were replenished?
Show the answer and why
That cannot be assumed. It says that a dish was added to the menu, without giving depletion as the reason.