Why does it matter? The priority tag meaning died a long time ago and even European carriers have stopped caring. LH used to be the best at it. Maybe they still are in FRA/MUC but I only ever transit there now, not stop. I flew LH and SN last week and my bag was middle to end. I remember SQ/TG also caring but I haven't flown them in a while (SQ segments coming up in October). Until they come up with a new tag and create yet another training and push for the priority tag meaning something this is all for naught IMO.
It's a nice perk to write down on a piece of paper and saying "priority baggage handling" but handling doesn't mean "one of the first out on the belt." Also doesn't mean white glove handling
As for the pic in the OP, my guess is they were double tagged to show they are all part of the same group travel.
-RM