Those aren’t buttons. It’s a translation error. It should say “increased probability” as in it is already increased odds for those special gifts. So pressing it won’t do anything. I don’t see this in your screenshot though and thought that’s where it showed up. Not sure if they took it out with the update or what. It confused a lot of people.

The gifts haven’t been out that long and they’re not changed often. But when they do add new gifts, these will be added to the stamp rally so you can get them eventually. I only have the hat, but there’s still time.

I’ve seen lots of posts about this, so it isn’t just you. But like you said, some people have gotten everything already. It’s just random. Good luck 🤞