Does my use of the word "عليها" (upon it/them) in the phrase "مستلزمات أي مشروع أعمله عليها صدقة ووقف" (the necessities of any project I undertake shall have upon them/it charity and endowment) make it a binding vow (نذر), knowing that I did not intend a vow and was neither jesting nor playing?

There is a scholarly difference of opinion regarding the expression "it is upon me [to do] such-and-such"; whether its ruling differs if the name of Allah is not mentioned or not. The correct view is that there is no difference. As for the saying "it is upon her," it is not a formula of commitment in the first place.