I updated my 13PM to 16.0.3 and all those services are working for me as normal. I'm assuming you've already tried powering down and rebooting the phone? You might also try a force restart:
If iPhone isn’t responding, try forcing it to restart.
support.apple.com
So what's actually happening, say, when you tap the voice dictation button in Messages? Does it make the sound indicating voice dictation has started but then fails to actually dictate your voice? Or does the button not even respond?