If I have a zone on my hob, for example, 260 mm in diameter, which provides 3.7 kWh at maximum power, how much of the zone needs to be covered to get the full 3.7 kWh power output from the zone?

To get maximum power from the entire zone, it must be completely covered by a pot or pan. This applies to all zone sizes if you want to achieve the maximum power from the respective zone.