What is the ruling of Islamic law regarding someone who made a covenant with Allah to abandon masturbation, and imposed punishments upon herself and invoked severe imprecations upon herself in the event of returning to it, then she did return to it and was unable to adhere to the punishments? What should she do to expiate her sin and avoid the fulfillment of her imprecations?

You erred by supplicating against yourself, for it violates the prohibition of the Prophet (peace be upon him). What you wrote on the paper is not a vow and does not bind you to anything. You must abandon this reprehensible habit in obedience to Allah and out of fear of His punishment. Prayer will help you with this, as will diligently engaging in remembrance (dhikr), increasing supererogatory acts of worship (nawafil), associating with righteous women, and avoiding anything that incites lust. You must also seek forgiveness for the sin you committed.