I've found that not overexplaining can also help me feel less ashamed about whatever the reason is. It helps remind me that in most cases, I myself do not need these details from someone in order to show them understanding and respect their boundaries*, so why bother assuming others need them from me to go about their day?
It's important for me to know my limits and reasons so that I can more realistically gauge what I can actually do without accidentally saying yes just to people-please, but on a casual basis, people say no without giving details all the time, it's fine.
Often in these cases the person who we (general we, not speaking for Lam) are trying to please/appease by overexplaining isn't even the person we are talking to, but a projection of our internalized shame/guilt/fear. And RSD can make that worse if we aren't aware of what's causing our feelings and what we can do about them.
*exceptions exist, the most obvious being that I cannot mindread someone else's boundaries, I do need to know what they are (though not why!) in order to account for them