As a follow up for others with this problem, here is what happened to me. I received my Series 3 watch yesterday. I unpaired my Series 2 from my iPhone, which also automatically backs it up to the iPhone. (Be sure you are using an encrypted backup or you could lose your saved Health App data. All iOS 11 iCloud backups are encrypted, but you must explicitly choose the setting to encrypt if backing up in iTunes.) I then paired my Series 3 to the iPhone and restored the backup from the misbehaving Series 2. I then paired the now-reset Series 2 watch to my wife's iPhone. Basically, both phones were started from factory settings. The Series 3 was restored from a backup and the Series 2 was set up from scratch. Both watches now display nightstand mode. That's the good news.
However, neither one will enter nightstand mode at the 45 degree angle of my charging stand. I must tip the Watches beyond that slope and then they will remain as I let them move back to 45 degrees. Given what others have said, and this experience, I think that Apple must have tweaked the angle at which the Watch enters nightstand mode, breaking a bunch of nightstands at the same time.
If you Watch won’t enter nightstand mode at all, then a backup, reset and restore is worth trying. If your Watch needs a higher angle than your charging stand to enter nightstand mode, then you'll just have to tip it farther manually for now. Perhaps Apple will tweak it back the way it was in a future release, if lots of us write Apple Suggestions asking for it.