The Apple Music Script delivers the composer. It uses the websize as source. Scripts that use the Itunes-API can't deliver the composer because the API knows no composer.
https://community.mp3tag.de/t/ws-apple-music/51184/62?u=poster
You should know that the delivered content with the Apple script is not always the composer but often the authors of a song (composer and lyricist together).
Another script that delivers the composer if it is available is the Deezer script.
https://community.mp3tag.de/t/ws-deezer/45537
Sometimes the Deezer script delivers the composer when the Apple script cannot and sometimes it is the other way round. You also have to lookup several editions of an album because not all deliver the composer. And sometimes you have to use several Apple Country versions to be successfull.
One would expect that Apple uses nearly the same database in diffferent countries but that is ovbiously not the case. I.e it is astonishing to find the composer of the songs of an US-country-album not with the US-script but maybe with the the German script.