I'm actually one of the screen reader users who did the testing. I can confirm that this is the problem I'm having when using the web interface.

I've tried this in Firefox, and I was able to read the audio player controls. I've tried using the carrot browsing in NVDA, and it made the navigation much better. However while using the carrot browsing, it did not play. It did play without it. Perhaps you may want to test conversant JS to see if it complies with WCAG standards. you could do so by going here.
https://webaim.org/resources/evalquickref/

Converse doesn't do anything fancy with audio/video, it uses the built-in HTML audio and video elements.

The issue seems to be that browsers don't support accessibility features for these built-in elements. 🙄

This article has more info:
https://developer.mozilla.org/en-US/docs/Learn/Accessibility/Multimedia

Looks like the workaround is to create a custom interface.