How do I balance team productivity with team wellbeing?

You are treating these two as enemies, and so they behave like enemies. Push output and wellbeing drops. Push wellbeing and output dips. When you default to output every time, you are quietly deciding that people are a resource to spend, and part of you knows that is not the whole truth. Over any short week, yes, they can pull against each other. But over a season, they are the same thing. A rested, respected team produces more, for longer, with fewer people walking out the door. Burnout is not free productivity. It is a loan you repay later with interest, in mistakes and in departures. Stop trying to hold both in perfect balance every single day. Instead, protect one clear thing that guards wellbeing and do not let output override it, whether that is no messages after hours or a real lunch break. Hold that line for a month and watch what it does to the work. You may find they were never truly opposed.