In Firefox, if I login to something in one Private Window, and open a second Private Window, my session is maintained (e.g. login to Protonmail on one, I open a second private window and I'm already logged in). So I assume Firefox is sharing cookies and whatnot between Private Windows.
Brave doesn't do this. If I login in one Private Window in Brave, the new Private Window presents me (correctly) with the login screen.
I've been through my Firefox settings with a fine-tooth comb and cannot identify anything that might be causing this. Hence I assume it is a bug.
(And yes, I mean new window, not a new tab)