I found the reason. If there is no API key the corresponding url parameter must not appear.
This is not working:
https://customer-api.open-meteo.com//v1/forecast?past_days=1&apikey=&minutely_15=shortwave_radiation,direct_normal_irradiance,temperature_2m,weather_code&forecast_days=3&timezone=UTC&latitude=47.11&longitude=11.11
The answer is
{"reason":"The supplied API key is invalid.","error":true}
Without the empty api key parameter this leads to a valid answer:
https://api.open-meteo.com/v1/forecast?past_days=1&minutely_15=shortwave_radiation,direct_normal_irradiance,temperature_2m,weather_code&forecast_days=3&timezone=UTC&latitude=47.11&longitude=11.11