Do I need to turn off my UPS when I power off my PC?
Or, put differently, is it okay for the UPS to be turned on all the time?
It is OK for the UPS to be on the whole time.
In fact, your UPS will last longer and be more reliable if it is not shut off regularly.
(Especially if the UPS has a small deep cell battery.)
An extremely minute amount of electricity will be consumed by the UPS - no differently than the battery of a laptop if it is always left plugged in.
You should follow the recommendations of the UPS manufacturer, but from my experience it is OK to leave the UPS on all the time. This will ensure the battery is kept fully charged in case you need it.
Otherwise, it will only charge when you turn it on and if you have a power outage, you may not have the full time on the UPS.