Sorry, I forgot to mention that you also need the work-rels included, because the works are linked to a recording also. So this will work:
So to get the composer you search the recording for <relation-list target-type="work">, and there you look for a work linked to the recording with the relation type “performance”. This will give you the work, which again will have relationships. Target type “artist” with relation type “composer” is what you are looking for.
If you prefer to work with JSON you can make the WS also return JSON data by appending the fmt=json parameter, e.g.