I've not been using the version with Tab Groups like this, so it will be interesting to see how much manual handling this possibly adds vs how readily one can differentiate between "Window 1-n" vs the current use of the active tab title.
Putting that aside for now, I was coming to this issue thinking it referred to how Private Windows could be more clearly indicated in the Window menu, text list, wherein I was going to suggest appending the Lock icon from SF Symbols to the left of all Private Window titles in the Window menu (approximating what's shown in the Address Bar itself.)
Likewise I'd suggest the same for Tab Hover Cards (AKA 'tooltips') on Private Tabs, and finally… perhaps going 1 step too far (?) in the title shown on tabs themselves, i.e. before they're hovered.