As usual, random diagrams found on the Internet are wrong.
You can't use white as a switched-hot. NEC 200.7(C)(2). White has the following priorities:
- If neutral is present in the cable, it must be white.
- If white is still available* and always-hot is being carried, it must be white, and marked.
- if white is still available, then it must be used NOT for a switched-hot, and marked.
- White can never, ever, ever be a switched-hot.
So you will need to re-jigger the wires on the switch spur to use white for one of the travelers. I recommend red for switched-hot, as that is a common color convention.
If it was me, I'd also use yellow tape to mark all travelers. 3-ways get a lot easier to understand when they look like this:
Also, in the metal receptacle box, you must ground the box first! Get a #10-32 screw in the pre-existing hole tapped in the box for that. When you have a surface mount steel box like that, you don't need to ground the receptacle - it will pick up ground off the box, via the direct metal-metal contact between receptacle yoke and box screw ear. (remove any of those plastic squares used to capture screws).
Switches can also pick up ground via their screw heads, even if their yokes aren't making hard flush metal-metal contact. Because they are switches :)
* think: 12/2/2 cable which has two whites.