Since the synonyms for this word "soft" are "gentle" or "quiet", you can interpret it as 静かな(Shizukana), which has both meanings. Therefore "soft music" will be 静かな音楽(Shizukana Ongaku). And it is generally used in Japan, as far as I've heard. Note that "light music" as a category may be translated as 軽音楽(Kei Ongaku) but it might be misunderstood in Japan. Indeed "light" means 軽 and "light music" can be 軽音楽, but what 軽音楽 or light music in Japan means is different from global definitions. We rather use it to mention Lock, Jazz or HEAVY metal music playing with electronic instruments. It is because 軽 also has the meaning of "cheap", and from some historical reason, we have viewed such instruments as cheap ones. We no longer have such a view today, but the word was left.

I don't understand "soft music", "sweet / light music"... Give me examples of world-famous musicians in the category.

soputo musik

"soft(or sweet) music" is "心地よい音楽(koko-chi yoi ongaku)" "light music" is ”軽音楽(Keiongaku)”

あまい音楽 (あまいおんがく) - Sweet music. 軽音楽 (けいおんがく) - Light music.