Basically, from testing it last not, the only sinks that work, are the Home Chef, Growing Together, Horse Rance, Rent, Love Struck, and Life/Death. The sim will pick up a dish/dishes and wash them like normal in those one. I've also noticed that those sinks are the only ones that offer the new in-game feature "Sink Type", where you can pick if it's the kitchen or bathroom sink. Every other sink from the other packs, including Base Game, no longer show "Sink Type" option, and that's how you can tell it's broken/bugged.
Please do not assume that I am not choosing the option to mark the sink as a 'kitchen' or 'bathroom' sink. I am saying that the option does not pop up at all at for those sinks. The same thing is happening to custom content sinks as well, that the option is not showing up. However, sims can still use these bugged sinks for washing their hands, brushing their teeth, and getting a drink of water. It is only when it's time to wash dishes that they will pick the dish up, and then place it back down.
I attached two photos to hopefully help :-)
The picture with the 'Sink Type' option is from Home Chef, and the picture with the black sink without the 'sink type' option is Base Game.