The photo of Seungmin wearing his necklace is at Chan's family home in Sydney, and it's probably a selfie, but there's another one in the set where the necklace chain is visible and someone else took the photo. Chan maybe, since it's his dog & his family's home? It's possible that other skz members were there too, but I don't think any of them have posted photos at Chan's family home from this most recent trip. (Although I have seen a grainy video of someone who's allegedly Lee Know being dragged along by Berry doggo enthusiastically taking him for a walk.)
Anyway all that waffling is to say: I think Bang Chan gave Seungmin that necklace. Probably not a birthday present, because Chan gave him a phone for his birthday.
At the Sydney concert, Bang Chan, Changbin and Seungmin talked about eating lamb chops cooked by Chan's dad, and Seungmin waved to Chan's family in the audience. Seungmin was insistent that Chan's dad should receive credit for the excellence of his lamb chops. I'm choosing to interpret this as competition to be the best son-in-law.
Okay judge me some more but: I have also seen a grainy photo of Bang Chan, Seungmin and Changbin together in Sydney, with none of the other members around.
Almost-entirely-baseless theory: only the three of them went to dinner at Chan's place and got fed the legendary lamb chops. (Or even ... stayed at Chan's place??)
Seungmin's new necklace is #skzSignificantJewellery to mark the occasion of an important family announcement e.g. hey fam we're engaged ahaha yeah I know 🤡🤡🤡
And Bang Chan's new triple cross pendant symbolises the polyam triad relationship with Seungmin and Changbin SHUT UP I KNOWWWWWW 🤡🤡🤡🤡🤡🤡