Thanks for all the replies! (And apologies for delayed response.)
@JDRoberts, ask me how I know this isn’t so… We have perhaps the crappiest ISP in the USA (their name rhymes with Suckeye Fable, near a city that is Spanish slang for toilet). It is their modem that disconnects several times a day and must be rebooted to restore Internet. Yes, it’s third-world service, and at ridiculous prices, because they have a monopoly.
So each time the SmartThings app is used to communicate with the outlet (to reboot the modem), there is never a Web connection, only a local/LAN one.
Writing this I just realized snooping the packets is a possibility – but still hoping for something more easily applied.
@rontalley, thanks for the ActionTiles suggestion. Since it’s web-based though, doesn’t appear it will work in this case.
@ sidjohn1, good to know there’s a hardware solution, thanks, but don’t want to invest in yet another gadget (too many already).
Pretty sure this comes down to a few data packets, maybe just a few bytes in a single packet; just need to know what data to send, and on what port.