Incognito window being one of the most used feature across the web browser. I wonder why they possess a dark theme?
I imagine that the reason behind having two separate themes for these browsing modes is to better reinforce communication to the user about which mode they are browsing in.
The difference in visual style is a subtle yet distinct visual cue to the user about which mode they are in.
It wouldn't be a nice experience if you wanted to browse 'incognito mode' but by accidental mistake you were using the regular mode only because the browser UI was the same.
As to why they chose a 'dark' theme and not an orange theme or something else, well I'm not 100% sure but I think they have just inversed the colours from the regular theme.
The dark colour of the buttons replaces the chrome fill and the chrome fill replaces the buttons. This is fairly standard practice as you don't have to adjust the colour palette, you just invert the primary & secondary colours.
It's a way to remind users what mode they're in. Kinda moot for the visually impaired user who relies on accessibility features and not color.
A better option would be to allow the user to assign their own color to incognito (or private mode) mode, reflecting personalization and cultural preferences on color.
Switching into this mode comes and announcing it with a handy message when you do so and its implication, such as with Google Chrome, Safari, or Firefox is the way to go.