Android shows when an app is using the microphone with a green indicator in the upper right corner -- I'm assuming iOS has something similar. How would apps get around this?

Easy: That indicator is not always on when the mic is.

Unless we're talking about an electret capsule with a physical LED wired into the supplying power rail that is switched off when the mic is not in use, you have to trust software.

And good luck with that after the patriot act. I am not implying the NSA has a microphone backdoor, but if they had and someone abused it, how would you know about it?

Listening in for keywords and only send text/audio when keywords are spoken isn't only good for ads, that would be dream of any intelligence agency. And since Snowden have been a few years.

But would you use it to show ads if you have access to such a backdoor? That's an easy way for your backdoor to be found out. Something like this, if it exists, would be too valuable to be used en masse.

Well if I am a secret service I could either try to force google to do it and risk a leak or I could find a way that there is something in it for them that has the benefit of providing plausible deniability?

> I am not implying the NSA has a microphone backdoor, but if they had and someone abused it, how would you know about it?

"Citizen four" by Edward Snowden.

How "hey siri" or "hey google" trigger phrases would work if they aren't listening?

Both iPhone and Android devices have dedicated low-power chips for detecting those exact wake words, which then wake up the rest of the phone.

Those chips do not log or transmit the audio they have access to.

Facebook Android app used to 10+ years ago I'm pretty sure

Yeah but that app was just nightmarishly bad, including an absolutely terrible approach to roll-your-own push notifications. Never attribute to malice that which can be explained by incompetence.