This morning I asked my wife something like “will you please get us a version of X that does Y” for a simple household product. A couple hours later she opens Instagram and sees an ad for “X that does Y”.
I take a look at Settings and see that my wife had 1. allowed Instagram access to the microphone, and 2. not asked the app not to track.
A bit of searching reveals enough of the same to make me think it is likely that Instagram is using microphone access to record, process, and make ad recommendations. Even when the app is in the background and/or your phone is locked.
It would be nice if someone with the right technical skills could do some research and reporting on this.