An app can't listen to the mic unless you grant mic permission, unless the app has been bestowed with magic entitlements by Apple. For example, Apple Clips is an app in the app store with magic entitlements that bypass cam&mic permission prompts. I have no idea why they brought out the big guns for that. Also, Uber was running with a magic screen scraping entitlement for a while, apparently to support Apple Watch in the early days.

Would also like to know this. And even if you did allow access, there would be the big red recording bar shown at the top of your screen when activated, right?

Nope, just tried this https://quiet.github.io/quiet-js on safari on my iphone. It just asks for permission, after that there is no indication that it's listening or not

Tried the same. It has red microphone indicator in the URL bar.

Safari, iOS 11.4

This is my understanding as well. Even if something has permissions granted to it by default as the system apps do, they’ll still show usage.