How do I cope with the constant vigilance of running a plant?

You can run the whole plant safely, and that competence costs you something real: you can never fully put it down. The vigilance that keeps everyone safe also keeps you from resting. That weariness you feel is the price of carrying something that genuinely matters, and it's worth naming honestly. But vigilance doesn't have to mean carrying it all alone, all the time. The strongest operations aren't the ones with one person watching everything. They're the ones where the watching is shared, where systems and trained people catch what one set of eyes would miss. Some of your exhaustion may be duty. Some of it may be a grip you haven't learned to loosen. Look at what only you are watching and ask what could be shared. Train someone to hold a piece of it. Build a check that doesn't depend on your attention. You'll never stop caring, and you shouldn't. But you can spread the weight so the vigilance doesn't hollow you out. A worn-down watchman protects no one well.