Challenge: Private Access Tokens (2022)

Previous discussions:

https://news.ycombinator.com/item?id=36862494

https://news.ycombinator.com/item?id=31751203

https://news.ycombinator.com/item?id=31669568

https://news.ycombinator.com/item?id=32950203

Apple's Private Access Tokens, implemented in 2022, have often been compared with Google's Web Integrity Environment. How are they the same, and how are they different?