Suggestions for a rule to shutdown the Hub on a UPS during power outage?

[SmartHomePrimer]

Assuming you have a way to trigger it, you can use @ogiewon 's code to Post to /hub/shutdown to port 8080

Is it possible to send an HTTP string on the local network?

Yes, this is very easy to accomplish on Hubitat's platform. It is really almost identical to ST's implementation. For example, take a look at my "HTTP Momentary Switch" Driver for Hubitat. Also, take a look at this WiKi post which highlights some of the simple changes necessary when porting apps/driver from ST to Hubitat.