How do I lead my people and the mission as one duty?

You have stopped seeing your people and the mission as a tug-of-war and started holding them as one duty. That is a mature place to lead from. You answer for both, and you lead from care, knowing that looking after your people and accomplishing the task are not enemies but two sides of the same responsibility. The strength of this is that it is usually true. People who are led with care perform better, endure more, and trust you when it counts. Care is not softness that competes with the mission; it is often what makes the mission possible. The rare moments when the two genuinely conflict are hard, but they are the exception, not the rule, and holding both as one duty is how you meet even those with integrity. Keep it real by making sure your care shows up in action, not just intention. This week, do one concrete thing for your people that costs you something, and be clear that it is in service of who you all are together. They will feel the difference between a leader who talks about care and one who leads from it. Be the second, consistently, and both the people and the mission are safe in your hands.