240, 480, three phase -- those are totally different beasts. I assume this is plain old residential 120v, with an earth bonded neutral.
240V split phase = earth bonded center tap/neutral, 120/120 commonly seen in homes. There are unfortunately too many terms for it. Not to be confused with a "real" polyphase supply like the 3 phase (208V, 240V, 480V, etc. and HV) commonly used for transmission and in commercial/industrial environments.
You are definitely not permitted to switch ONLY the neutral. That's universally bad. Switching both seems fairly common practice in devices. Obviously not so much in fixed wiring.
My experience has been that the NEC is full of "once upon a time, in some freak occurrence, this resulted in somebody getting killed or a house burning down" types of rules that have little basis in actual reality. That's not to say that the NEC is garbage: quite a bit of it is good electrical practice, but there seem to be some elements that are based upon hearsay and fear.
Note that I'm not an electrician, and you should always follow the NEC when required.
I'd probably opt for switching both: switching just the hot requires only a single failure that is relatively common to potentially result in a dangerous situation (reversed hot/neutral) while switching both requires a double failure one of which seems less likely (broken relay with hot always engaged and the user doing something dumb as a result of misinformation).
FWIW, you might add a suitably sized fuse on the hot side before the relay. This will prevent an overload of the relay from resulting in a dangerous situation as I doubt your relay is rated for 15-20A (and even if it is, a fuse never hurts) and will also catch the (unlikely) failure of the two poles of the relay shorting together. The diode on the relay coil is not strictly required in this situation since there is no local switching component to protect, and the SMPS output is inherently protected from small inductive kickbacks, but it doesn't hurt, and I'd probably leave it there.