I arrived to this page after searching for this exact issue. I would be rereading a text message and the hang up sound (what I called it) would happen for several weeks now.
I noticed the voice to text microphone on the bottom flash the last time it happened, so I knew that was where it was coming from.
After reading all of the comments, I went back to try and recreate the noise and was able to successfully recreate it only by going to the text thread, clicking on the contact, then going to info, scrolling all the way to the bottom and then going back to the text.
I heard the noise, then saw that voice to text microphone on the bottom of the text change to: 00.00. It was a timer…waiting for my voice to start. I was only able to recreate the noise a time or two, but it most definitely has to do with the voice to text microphone.
I wondered the same as others: “does in mean the other person is in the same text as me?” “Did I accidentally share my location with this contact?” Ultimately, I think those are incorrect. It’s just the iPhone attempting to record voice to text, for whatever reason.