My Safari is 10.0.2 (11602.3.12.0.1), but it was just released yesterday. (Note the red. Is your version number a typo?)
Wouldn't it be strange for the macOS update to affect Safari without changing its version number?
Just to see if we're on the same page: in the Passwords pref pane I check a box that says "Show passwords for selected websites", I'm asked to authenticate, and even if I only selected one website to start, I can then click on all other websites and see their passwords. (That's been my experience since Safari 10 was released.)
Last edited by artie505; 12/14/16 04:49 PM. Reason: Expand
