It looks like one needs to install the BrowserCheck extension in each installed browser. (Tested with Mac.)
On my MacBook Pro running macOS 10.13.6 (latest version supported on this Mac), I installed BrowserCheck in both Chrome and Firefox. The scans found one issue (Silverlight out of date; I updated Silverlight; THANKS!).
When I then attempted to install BrowserCheck in Safari, the installation failed with error message "Safari can't install this extension". See attached screenshot.
I'm running as standard user, and as expected, entered the admin password to perform this installation.
Just out of pure cussedness, and hoping for a different result when doing the same thing again (<grin>) I tried this three times.
Hoping for a way to make this work. Any ideas?
Thanks, Bob Stromberg