I am trying to use a stream for something and I think I have a conceptual misunderstanding. I am trying to take an array, convert it to a stream, and .forEach item in the array
What you are looking for is called the map operation:
Thing[] functionedThings = Arrays.stream(things).map(thing -> functionWithReturn(thing)).toArray(Thing[]::new);
This method is used to map an object to another object; quoting the Javadoc, which says it better:
Returns a stream consisting of the results of applying the given function to the elements of this stream.
Note that the Stream is converted back to an array using the toArray(generator) method; the generator used is a function (it is actually a method reference here) returning a new Thing array.