Is it obligatory to give out one-third of the bonus after the salary system has been changed, and is giving out one-third of the salary for the sake of Allah considered a vow?

A vow is not binding unless it is expressed verbally in a way that indicates commitment, such as "A vow is upon me" or "For Allah, I owe such and such." If you did not utter the words that make a vow binding, then this is not a vow that must be fulfilled. You are permitted to give in charity a third, or less, or not at all. And if you do give in charity, then Allah Almighty will compensate you.