It would seem that the power of an oath depends on how successfully it alters and/or cements belief. Is it correct to say it’s not the oath itself that binds, but the effect it has on the beliefs of oath takers, oath administrators, and oath witnesses?

This is a useful perspective to consider because it is very much the case that taking an oath will create new beliefs, and perhaps challenge preexisting ones. So the sum total of what happens in response to having taken an oath will depend on the strength of preexisting beliefs, whether they are positive or negative, in alignment with the goals of the new oath being taken, or in conflict, so there are many potential complications here. And here again there can be a fork in the road, so to speak, where an oath might raise someone up in helping them to reinforce good conduct and positive attributes like service, loyalty, honesty, and integrity, diligence, and commitment, or it might become an entrapment in some way by creating a significant source of pressure and harmful influence on otherwise good instincts and divine impulses, or divine perspectives that might be loftier than the aims of the organization one is serving with the oath, and bring the person into conflict with their ethics and morality, and thus tempt them to compromise, lower their standards, and embark on a slippery slope from which they may not recover. In some respects, the beliefs that govern people's choices in the moment are the ones that shout the loudest, not necessarily the ones that are in the best divine alignment, given the mixed makeup of human beings as a consequence of being in a corrupt environment, and among so many who themselves are corrupt and out of divine alignment, to serve as bad examples, and influences from the time an infant is born until they eventually pass on. This is quite a challenge for everyone to make their way under such circumstances. There are many temptations, many risks, many encounters with negativity, and many reasons one can fail. This will make oaths an incentive for maintaining the straight and narrow, leading to success if one is fortunate, or a further liability that might well be regretted as a measure of a fall from grace when they fail to live up to that oath's promises and obligations. Beliefs have some malleability but are quite powerful as an influence on things. So an important factor to keep in mind about people taking oaths is that all are not equal stepping up to take their pledge, whatever it might be—they will vary in their makeup and the many attributes defining character, reliability, and divine alignment, making them more or less likely to follow through and live up to the oath they take.