How do I build real confidence in the safety of my work?

You have arrived at a grounded, earned confidence: you trust the care in your work because you know your calculations hold, since you do them right every time. That is not arrogance and it is not luck. It is the quiet certainty that comes from doing a demanding job properly, over and over, until the trust is deserved. What makes your confidence solid is that it rests on action, not on hope. You are not telling yourself it will probably be fine. You know it holds because you did the work that makes it hold. That is the only kind of confidence worth having in a trade where the stakes are real, and it is the kind that lets you sleep. Keep it anchored to the practice. Confidence in this work is renewed by continuing to earn it, one careful job at a time, never by getting comfortable enough to coast. Do them right, every time, as you have been, and the trust stays honest. You have built something dependable, in your work and in yourself. Keep doing the work that keeps it true.