Thanks for checking. Now that we know the cause of the issue, we've made one step forward.I tested it and got the same result—the warning sound goes off, it stops, and in that state it doesn’t go into standby, the screen just stays on. I wish it would switch to standby in that situation. I often forget and leave it on when I go out, so I hope this can be fixed in a future update.
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Since you are using a Chromecast, simply stopping YouTube Music on your phone once before going out should solve the issue for now.
I will report back here if I hear back from the team on my ticket.