Do my supplication and promise to God not to repeat a sin count as a vow, and what is its ruling?

No matter how great a sin a servant commits, if they repent with a sincere repentance that fulfills its conditions, Allah will accept their repentance. Repentance involves abandoning the sin, regretting having committed it, and resolving not to return to it. The questioner's statement: "O Allah, if You forgive me, then I will not repeat such deeds" is not a form of vow, because a vow is contracted with wording that signifies commitment. If we consider it a metonymy with intention, it is contingent upon forgiveness, which is an unseen matter whose occurrence cannot be ascertained. If we adopt the view that conditioning upon something whose reality is unknown is akin to not conditioning at all, then what is vowed here is an obligation, and a vow of an obligation is not binding according to the majority of scholars. However, the more cautious approach is the view of Shaykh al-Islam regarding the obligation of an expiation for breaking an oath when breaking a vow of an obligation. The questioner's statement: "And I swear that this is a Muslim's promise to his Lord" has no consequences because it is a statement about a factual matter. We advise the questioner to repent, distance themselves from paths that lead to disobedience, and seek help from righteous companionship.