Leadership is noticing the kid sitting alone and not needing a reason to go over.

Two things are happening here and the first one is noticing at all, which most people in a room genuinely do not. The second is going over without needing a reason that would hold up if questioned. The moment it becomes a favor it turns into something done to a person rather than with them, and everyone can feel the difference. Sitting down and talking about something normal is the whole action.

Do it once this week, and keep it light. Ask about the thing they are doing, not about why they are alone. Include the same person again next week if it went fine.