If there was a worldwide standard, then WMO would have imposed it to its members. Here are the definitions in the American (NOAA/NWS) standard
(summarized at NJWeatherScan, initially from manuals like this one (PDF page 66, page label 58):
Light rain: falling rate of less than 2.54 mm/h. This would be < 0.042 mm/min.
Moderate rain: falling rate of more than 2.8 mm/h, but less than 7.6 mm/h. This would be 0.042 mm/min - 0.127 mm/min.
Heavy rain: falling rate of more than 7.6 mm/h. This would be > 0.127 mm/min.
So clearly different standards compared to the DWD answer (note: 1 l/m² is equivalent to 1mm). Nowadays, automated weather stations use rain gauges with sensors, so a modern station with the computer inside has a clear and accurate computation of rain/snow falling rates. But there is no universal standards.