Is expiation (kaffarah) obligatory for one who swore an oath that they would "try" to abandon something, but was unable to do so?

The oath mentioned in the question pertains to a breach, and the determinant of a breach is the intention of the one who swore the oath. If by your words you intended to abandon something, then by doing that thing, you have breached your oath. If you had no specific intention, then fulfilling the oath requires exerting effort in attempting to abandon it. If you did not exert effort in attempting to abandon it, then you have breached your oath, and you must offer the expiation mentioned in His (the Almighty's) saying: (So its expiation is the feeding of ten poor people from the average of that which you feed your [own] families or clothing them or the freeing of a slave. But whoever does not find [anything], then [it is] fasting for three days. That is the expiation for your oaths when you have sworn. And guard your oaths) [Al-Ma'idah: 89].

If the thing is unlawful, it must be abandoned absolutely, even if no oath was made to abandon it. And if it was permissible and you attempted to abandon it, then your oath has been fulfilled, and no expiation is due upon you.