Hi Marius,
In my case, I retrieve a GHI forecast for the day-ahead (e.g., on Tuesday, get the forecasted hourly GHI for Wednesday), along with 2m temperature and 10m wind speed, and use that to model power. You could also get the 0-hour-ahead forecast for something like real-time power, but almost all forecast NWP models (NWP = numerical weather prediction) take an hour or more for the weather agencies to run, so there is some lag.
And whether you want to get GHI directly from the NWP depends on the NWP and your choice. As Cliff and Jurand mentioned, some forecasters use cloud cover and an additional model to estimate GHI. There are also considerations around tie interval length that are NWP-specific. For example, many NWPs have a 3-hour interval, and forecasters will post-process them to interpolate to hourly using a clear-sky model. Open-meteo.com seems to do all of this for you, but you would have to look into their documentation/source code to see what is actually going on.
And another point for clarification, I don't use clear sky GHI directly for modeling a power forecast.
Will