Isn't this a Chrome-specific "Smart-Lock" or "Auto Sign-In" dialog? It shows multiple selectable users in a modal dialog, AFAIK Windows.Alert() is not able to do this.

That is correct, it is just opening Chrome's password manager:

  await navigator.credentials.get({password:true})

https://developers.google.com/web/fundamentals/security/cred...

I do think it is odd that this API will present the UI without any user interaction first. (Doesn't require a tap/click to open.)

As mentioned in the tweet's replies, this isn't true at all. I definitely was a bit shocked to see my username appear in incognito, but this isn't a window.alert. Twitter has no access to your username in incognito.