What is incumbent upon me if I supplicated to Allah to be among the righteous upon my recovery, without recalling the exact wording, and believing it to be a promise and not a vow, and can expiation be made for this vow now or after recovery?

The mentioned wording does not constitute a vow, as it does not signify commitment, nor did the questioner intend it as such. Therefore, it is a promise that does not incur expiation if broken. A Muslim must be among the righteous by performing obligations and avoiding prohibitions. If one falls short, they must repent and seek forgiveness, for Allah Almighty says: "And those who, when they commit an indecency or wrong themselves [with sin], remember Allah and ask forgiveness for their sins - and who can forgive sins except Allah? - and [who] do not persist in what they have done while they know. Those - their reward is forgiveness from their Lord and gardens beneath which rivers flow, wherein they will abide eternally; and excellent is the reward of the [righteous] workers."