So its not that the Has Authority specifically is affecting the Stream but what is happening is due to the Pure nodes you have there.
With this section here on the Client you use the Bool to check whether to spawn which runs the Random Int in Stream. That bool is false so it continues.
Whereas on the server this returns true and therefore re runs the Random Int From Stream for each other pin you pull out from that node.
To solve this, cache the returned struct from the Get and use that instead of breaking it as you have there.
