Not only do those books still exist, but there's more of them, they're more diverse, and more are being written by people who belong to those cultures (rather than well-meaning white researchers). This was just what I found on a five minute cursory walk through the children's area of a small, rural library - there's way more than this, and that's not even touching on the hundreds, thousands of picture books, chapter books, comics, and YA about, by, and for people of all backgrounds. This was just one shelf!
Don't let nostalgia bias fool you into thinking that children's books haven't gotten more diverse because it is very much the opposite. If you haven't heard of the organization We Need Diverse Books, they were formed over a decade ago and they're awesome - they're not the only reason things have improved but they're a big part of why.