Is repeating the attempt to pass the driving test after seven years of swearing not to try again – in the event of failure – considered a breach of an oath that necessitates a tormented conscience and constant anxiety, despite giving charity and performing Umrah?

There is no objection to retaking the driving test after having sworn not to retake it. You are required to offer expiation for breaking an oath, based on the Prophet's (peace and blessings be upon him) saying: "Whoever takes an oath and then sees something better than it, let him do that which is better and expiate for his oath."