For those of us unfamiliar, can you describe the resulting UI pattern? Do you give focus to the password field and then tap a button at the top of the notification shade which automatically types (or gives a choice, if multiple are saved) whatever the password manager has for that site? I'm slightly surprised that something running in that context would know what site the browser has open.

It appears to work... I wasn't even really aware I could add such a thing until the GP comment. I also managed to get the integrated use working... apparently there's now a separate config option for "chrome integration" and "brave integration" etc.

It reads the browser URL through an accessibility service.