Alright, what I thought was some dress button was very likely the skeleton of the blue button(Porpita species), or the blue button jelly as some people will call it. (Thanks to Mosura who suggested I look up Porpita!)
Wikipedia says this: This "animal" is actually a colony of animals. Each of those radiating tentacles is actually one individual animal. These guys are "house mates" that share the same air-filled disc made of chitin. (The brownish disc does look like the ones I photographed.) And a blue button is not a jelly. So calling it a blue button jelly is a bit misleading. After all, a jelly is an animal, not a colony. Interesting! I have seen these dead blue buttons only once on the beach. Although Wikipedia says "mass beaching is common", I didn't see many of them that time. And that was a couple of weeks ago. I don't think I have come across any during my last two visits to the beach. In fact, it is interesting that one or two months ago, I also saw heaps of blue bottles on the shore once, and then I just don't see them anymore, not even one.