In the process by which the formation of self-efficacy through a sense of accomplishment strengthens the moral self, should the 'firm foundation of stability' that resolves existential anxiety be regarded, from a deontological standpoint, as a condition for fulfilling which specific moral duties?

First, the acceptance-and-struggle framework stands in direct opposition to deontology. Because humans have limited cognitive capacity, we are never able to fulfill our moral duties at all times. I think that what we regard as a duty (that is, a decision that appears rational at the societal, long-term, or macro level) can only be satisfied when specific environmental conditions or the cognitive resources available at the time allow compliance with that duty. Still, to explain in a way that resonates well with the conventional deontological perspective: when a solid foundation of stability is in place, the likelihood that we rely on irrational decisions driven by anxiety decreases. This is because a solid foundation of stability is a device for strengthening the influence of System 2 in the System 1 versus System 2 framework of behavioral economics, and it prepares the environment in which more rational, reasoned inference can take place. Given that the main reason we violate moral duties, even while recognizing them as rational, is the risk that is perceived as very important and urgent to us, a foundation of stability that keeps the perception of this risk from being exaggerated and distorted is one of the good preparations for fulfilling duty.