Is it obligatory to offer an expiation (kaffarah) or charity (sadaqah) to seek forgiveness for not performing istinja' after urinating in the past?

If you repent with a sincere repentance that fulfills its conditions, then Allah will accept your repentance and pardon your sins. As for the prayers you performed while being defiled and aware of the obligation to remove the impurity, they are invalid and do not discharge the obligation. You must make up these prayers, which are a debt upon you, even if it means making up many prayers. If you are unable to determine their number, then exert your best effort until you achieve certainty or a strong presumption that your obligation has been discharged.