Thanks for the post-back. Have you ran a full system scan with Malwarebytes? Personally, no matter what version of Norton I’ve had installed backup has never asked for these or other password credentials when running a backup. Certainly not passwords that may have been or are stored within a browser. Has this occurred again since your posting when running a backup while NOT connected to the internet via any browser?
I also found an older thread here on the forums that is somewhat related to your issue. It too involves Google Chrome accessing login data for the logged in user.
Have you ever set a password within Norton to protect changing any of its setting? Have you reviewed your Norton history for more information about the event?
SA