My team rewards looking busy instead of doing real work. How do I change that?

Busyness is easy to see and easy to praise. Fast replies, full calendars, people who always seem to be running. Real work is quieter and slower, and it does not always look impressive in the moment. If your culture rewards the visible motion, people will give you motion, and the deep work will thin out. You already see your own hand in this. You modelled it, and the team read the signal correctly. That is not a reason to feel ashamed. It is the reason you have real power here. If your behaviour taught the pattern, your behaviour can begin to teach a new one. Pick one thing that matters and praise the result, not the effort around it. Out loud, in front of the team, honour the person who went quiet for a week and came back with something that mattered. Protect a block of time where being unreachable is allowed. When people see that outcomes get the applause, they will stop performing the busyness.