Is this considered a vain oath (yamin laghw) for which expiation (kaffarah) is due if the wife breaks it, or is the oath annulled over time, taking into account Allah Almighty’s saying: "Allah will not hold you accountable for what is vain in your oaths"?

This is a binding oath that is not invalidated by the passage of time. Since the matter sworn upon is impermissible, as it infringes upon the property of another without their permission, you must offer expiation for your oath. However, you will not be considered to have broken your oath unless you fail to do what you swore to do when its cause arises. The expiation for an oath is explained in Fatwa no. 31077.