This is burnout, and it won't resolve itself

Not recovering on days off, months of it, cynicism about work you used to care about, and disrupted sleep is the recognised pattern. Willpower does not fix it and neither does a week away.

Talk to a doctor — the sleep component alone is worth medical advice. Then have the conversation at work about workload rather than performance. If neither is possible, that is information about the job rather than about you.