What role does an individual's completing small everyday goals, such as minor rules or daily quests, play in forming a moral self?

I think it would help strengthen the moral self. Repeating the experience of solving a problem of a size one can actually solve and gaining a sense of accomplishment helps form a positive sense of self-efficacy, which seems likely to serve as a foundation for affirming modern morality. It reinforces the belief that a person can change the world for the better through their own will. However, if this process is not accompanied by a firm sense of attachment, there is a concern that it could blindly intensify the pursuit of modern ideals. To minimize such negative concerns, a solid foundation of stability needs to be formed by resolving existential anxiety.