I have an iPhone 13 on iOS 16.0.2 and same problem here. I have already reset "Hey Siri", Dictation, network settings, the iPhone (volume up and hold power on button)...and it continues exactly the same.
It seems like Siri activates but she doesn't "listen" because after finishing the command it starts like "wait a moment"...."I'am on it...".....and finally "I have had some problems"...
The dictation exactly the same. I push the button, the icon appears with a little cross and then nothing happens.
On the other hand, I have an iPhone XS on iOS 16.1 beta 4 and an Apple Watch Series 4 (WatchOS 9) and some homepods mini and in all devices it's correctly working...
¿Solution?