As I understood not ANY website can see it. But the same website can see it regardless if you reset your identity in Tor Browser.
So it persists between anonymous sessions.
So you could connect User A that logged out and reset the identity to User B who believed was using a fresh anonymous session and logged in afterwards.
No, it does allow identification across different websites (the article says "both cross-origin and same-origin tracking"). Both websites just need to create some databases with the same names. Since the databases are origin-scoped, these aren't the same databases, so you can't just write some data into one and read it on another website. But it turns out that if two websites use the same names for all these databases, the order the list of databases is returned in is random-per-user but the same regardless of website.
So it persists between anonymous sessions. So you could connect User A that logged out and reset the identity to User B who believed was using a fresh anonymous session and logged in afterwards.