Anker Support Team responded to my email:
SoundCore Support Team
5:18 AM (4 hours ago)
So sorry for the delayed response. I've been caught up by the work recently.
Please know if you put the earbuds into the charging case when the case had only one dot out of three of the battery, the earbuds will be off, then its rest battery won't be drained. But if the battery is totally used, then the earbuds will be triggered to power on, and it will try to pair to the last device it was connected to. I am afraid it is designed this way and currently, we have no way to change this for the SoundCore Liberty Air headphone. So sorry for the inconvenience!
As far as I know, some competitors are able to make their earbuds shut off all the time in the charging case, however, they also need to turn on the earbuds manually. I have forwarded your forum link to our product manager to consider. I am sure they will consider this feature for newer models in the future.
Meanwhile, except for this feature, may I know if this headphone still works fine for you? Please be assured we always stand by our products and provide an 18-month warranty for all quality issues.
Looking forward to your reply.
It looks to me it depends whether you put them back in the case when the case has or has not battery on it.
On my side, I have verified that even when the case has no charge, they turn off when I put the battery back in, so there must be some load applied to it. But if you leave it overnight, it will discharge.