Is performing a two-rak'ah prayer with the intention of fulfilling a need and persistently doing so for over a year considered an innovation, or is it a supererogatory prayer?

Voluntary prayer is good and a righteous deed, as long as it is not performed during the prohibited times. A person should not adopt a permanent litany of absolute voluntary prayer unless they are highly confident they can maintain it. Maintaining two rak'ahs is a good thing. The advice for someone accustomed to such a prayer is to leverage this habit and utilize it for the Sunnah, by shifting these two rak'ahs to a time encouraged by Islamic law. The best time for this would be at night, to attain the reward of both voluntary prayer and the Sunnah. Allah the Almighty says: "There has certainly been for you in the Messenger of Allah an excellent pattern for anyone whose hope is in Allah and the Last Day and [who] remembers Allah often."