Server vs Client access

The Server is the only thing that can access ServerScriptService and the ServerStorage. The client cannot access these items which further secures objects inside those services.

The reason Wings comes back nil is because the client cannot see objects inside the ServerStorage.

Replicating Accessories to Others

We need to use a RemoteEvent for the client to be able to communicate with the server. Once the client presses the GUI button, we can use the RemoteEvent to :FireServer(), basically sending a signal to the server to do something.

local humanoid = Character.Humanoid

Button.MouseButton1Click:Connect(function()
    local arg1 = humanoid
    local arg2 = 'Wings'
    RemoteEvent:FireServer(arg1, arg2)
end)

In order to make this work the server has to listen for signals that clients are giving them. OnServerEvent will listen for every time a LocalScript runs :FireServer() on a RemoteEvent. From there we can clone and attach things and it'll replicate on everyone's screen.

RemoteEvent.OnServerEvent:Connect(function(player, arg1, arg2)
    local playerWho_FireServer = player
    local humanoid = arg1
    local HatRequest = arg2
    
    local Hat = ServerStorage:FindFirstChild(HatRequest)
    if (Hat) then
	    --clone, parent to char, Humanoid:AddAccessory()
    end
end)

Now I named these variables to make sure you understand what is going on. We are sending specific arguments the the Server so the Server knows what Humanoid needs what Hat. What we did here is the client sent its HumanoidObject as well as a String telling which hat to look for in the ServerStorage. The Server then looks for the hat and checks if it exists. Pretty sure you can move on from there.

Good luck!