Is that new in iOS 15? They never used to - it was something I missed when switching from the Nokia ecosystem (Symbian/Meego) to iOS. It's nice for turning your phone off at night but still using it as an alarm clock.

Edit: Just tested it. Sadly it still doesn't work. iOS 15 on an iPhone SE (2016).

Yeah I’d be really surprised if alarms worked while the phone is powered off.

It is Real Time Clock (RTC) chip just as found in ATX motherboards since like 1997, very primitive and low powered, so it can't spy on you, just provides autonomous time source. Power-on alarm(s) is RTC's feature as well, merely comparing preset alarm time register(s) with current time register.

Until the alarm on your “powered off” iOS 15 phone goes off in the middle of the chamber music concert.

I don’t understand why the “silent” switch doesn’t mean “completely silent”.

Why would you set an alarm for the middle of chamber music concert?