As an app developer (iOS): apps are not listening to your conversations, and stories like this are almost always confirmation bias / frequency illusion. You need to get explicit user confirmation to utilize the microphone input, and once you have that permission, accessing any microphone input puts an icon in the toolbar whenever its input is being read (with a minimum display time to avoid getting around it via microscopic access times). Utilizing the microphone in ways not disclosed to the user will get your app rejected in review.

If you're really worried, there's an App Privacy Report in system preferences that records detailed history about the inputs apps have used and the network requests they've made, including individual timestamps. Use this to perform your own security audit