I think that when an apology is not promptly offered, especially for an egregious mistake, it's very telling.

It really is, that to me is a red flag on anyone... whether romantic, friendly, professional, acquaintance....

At that point I have acknowledged the other person's ruffled feathers and it's about "where do we go from here," if it's a person I even want to have that conversation with.

and the "where do we go from here" conversation is one that works only if both people are willing to let go of any negative feelings they had about a situation and heal things. Mutual humility is favorable in the pursuit of resolution and concord between contentious parties.

Going beyond just recognizing someone's ruffled feathers, discerning how our own actions were unskillful in that they put as odds with another: If we can discern that, then apologizing becomes genuine, and we benefit as well as the other. We apologize healing each of us benefitting us in the now and then seeing how our actions were the cause of previous conflict, we can abandon those actions so it doesn't happen again–that benefits ourselves in the longterm. Of course in the case where we did have good discernment and saw that our actions were not the cause of someone's contentiousness, then there is nothing we can do.