Is there any way an iOS app can access the mic/camera without the user's knowledge?
The first attempt by any app to access the microphone or camera will cause an OS-level confirmation dialog to grant permission. This adds the app to that list with the ability to grant/revoke the permission.
There are no exceptions to this; these are the only APIs that Apple makes available.
Also note that there is a ‘speech recognition’ category in Privacy which you may consider access to the microphone, albeit just what words are spoken as text if any. iOS does the speech recognition on behalf of the app; if the app does the recognition, that’s the generic Microphone category of access.