Make sure you click inspect element on the website you load not on the default page from the safe browser. The developer tools window should have the url you are using at the top of the window, not beaker:shell-window.
This changes everything. Thanks! It seems I’m too used to Firefox way of working - SafeBrowser is different in many ways (no F5, no F6, no Ctrl-PgUp/Ctrl-PgDn,…)