What type of oath is this, and what is its expiation, if any? If there is none, what should I do with these purchases?

This oath is binding, and it is an oath of righteousness. If the one who swore the oath realizes its error or wishes to retract it, he can absolve himself by performing an expiation for an oath and doing what he swore to do, based on the saying of the Messenger of Allah, peace and blessings be upon him: "Whoever swears an oath and then sees something better than it, let him expiate for his oath and do it," and his saying: "And I swear by Allah, if Allah wills, I will not swear an oath and then see something better than it, except that I will do what is better and absolve myself of it."

Therefore, you can pay for your wife's purchases and expiate for your oath by feeding ten poor persons or clothing them, or by freeing a slave. If you cannot find any of these, then fast for three days.