What is the ruling on commissioning someone to buy goods that I swore not to buy, in order to release myself from my oath?

The apparent conclusion is that you owe an expiation for breaking an oath (kaffarat yameen), because your intention was that the goods would not enter into your possession. However, if you intended not to directly purchase it yourself, but through your agent, then there is no expiation due upon you.

Whoever swears an oath not to do something, then appoints someone else to do it on their behalf, has broken their oath, unless they intended to do it themselves directly.

What is incumbent upon you is an expiation for breaking an oath (kaffarat yameen). You have the choice between feeding ten poor persons, clothing them, or freeing a slave. If you are unable to do any of these, then you must fast for three days.