Can you use another microphone (wired or wireless/Bluetooth) with Voice Control?
I have this problem with each of my devices - iPhone 15 Pro Max, iPad Air, and iMac:
Voice Control in Accessibility only accepts commands or dictation from the device’s built-in microphone.
I bought the only microphone I could find that, in effect, mutes the sound of my voice so that those around me do not hear what I am saying. It is the Privo by Talk Technologies (https://talktech.com/shop/stenomask-store/privo-wireless/), by a company that makes microphones for court reporters to use to dictate quietly in courtrooms. (I tried their wired microphone first; it did not work at all with voice control, though it did work with various apps. I was advised that Voice Control should work with Bluetooth, so I returned the wired version and invested in the Privo)
The Privo works just fine for phone calls, and for dictation in apps such as Notes, Pages, etc. Yet when I turn on Voice Control, the software does not recognize the Privo even though it shows as connected in Bluetooth settings. It seems that the voice control software only listens through the device’s microphone.
Is there a way to use Voice Control with a microphone that is not built in?
iPhone 15 Pro Max, iOS 17
> System Settings, click Accessibility 
in the sidebar, then click Voice Control on the right. (You may need to scroll down.)