it's been like that on all non android walkmans, the default power off is a sleep mode, giving one of the fastest wake up you can find so that you don't have to wait if you have to put it aside several times a day. but that's at the cost of battery going down all that time it's off.
so sony set it to really turn off after ... 24h might be right, I never actually timed it. that saves us from coming back to a dead DAP after some days in a drawer. so it's very much not a problem nor a bug.
about the library update, the message is only telling that the DAP is kind of loading the library list so that browsing is fast. if you look at how long it takes for the supposed scan, you realize that it has nothing to do with the actual library update done with a new SD card(that can take several minutes depending on the files and the card).