After registering your email address with the Audacy app, when listening to a Rewind enabled live content, the "continue listening feature" allows you to resume listening across devices from the exact moment you left off another device.
If you wish to resume live listening, then you can simply select the "Back to live" button, which is located below, to the upper right of the time bar. This will always take you to the live broadcast on the station that you are listening to.