Is what was mentioned in the supplication, “O Lord, assist me so that I may give charity to the poor daily,” along with the mention of several acts of obedience, considered a vow or a promise that dissolves upon the first transgression?

A vow is only binding if it is expressed in a form that indicates commitment, such as saying: "It is for Allah upon me so and so," or "I vowed to Allah so and so," or "If Allah cures me or helps me, then upon me is so and so." The mentioned wording does not fall into this category, so nothing is binding by it. Attaching a vow to a condition is disliked, so one should not proceed with it.