WoW: How do I get the stats/effect of an item?

I was trying to find it in the documentations but unfortunately I cannot find any. Did I miss it somewhere?

There is no way of doing that using the Game data endpoints. However there is an undocumented feature on the community endpoint. (it was mentioned in a blue post on the old forums).

You can append a list of bonus ids to the queryString like this:
.../item/123?access_token=token&bl=1111,2222,3333

When using this feature the returned json changes and include additional info based on bonuses. You might get extra sockets, different drop context, and so on