I know covering feet is a part of the women’s hijab. But can a woman wear skin tone socks to cover the feet or does that disregard the purpose of socks as it looks like the woman’s skin color?

If the socks are transparent then it is haraam.
If a woman is wearing non transparent socks which are skin colour but it is coupled with a dress that is attractive and the socks add to it in such a way that it attracts attention of the opposite gender then again it is haraam.
If the socks are non transparent and cannot be mistaken for a woman's foot and do not draw attention of the opposite gender then there is no problem in wearing them