It is my understanding that many of the deep sleep messages were programming errors and you weren't actually going into deep sleep mode. I got the messages, too, but the car functioned fine. I read something about this recently but I don't recall where.
Auto start / stop is very complex. There are posts in this forum that list the criteria. During the summer, mine seldom kicks in. But that's okay. If auto start / stop doesn't kick in, it doesn't necessarily indicate a bad battery.
If the dealer has tested your battery and it shows good, I wouldn't fret it. Take the trip and enjoy the drive.