How do I cope with being the invisible person who keeps everything running?

You can untangle almost any software problem, and because you do it so well, no one sees it. Things simply keep working, and the work that keeps them working stays invisible, and so do you. That tiredness is fair. It is hard to pour real skill into something that only gets noticed when it fails. Here is a quiet truth about your kind of work: its success is silence. When you do it perfectly, nothing happens, and nothing happening does not make headlines. That does not mean your value is not real. It means the world often forgets to thank the people who prevent disasters rather than clean them up. One step: do not wait to be noticed; name your own contribution plainly, to yourself and, when it fits, to others. Keep a simple record of what you kept running. You are not invisible to the truth of things. Make sure you, at least, do not lose sight of it either.