@Hbib it’s always a smart idea to share things like which OS you’re on. I’m assuming you are speaking of desktop based on some things you said, but always good to leave no doubt.
Anyway, on desktop, just go to brave://flags and enable Auto Dark Mode for Web Contents. Just Enabled tends to be good enough, but you can experiment with other one based on your needs.
When not using this flag, you just put Brave in dark mode and how websites load will depend on how they are coded. If they have dark mode, then usually it starts to load that way to match your browser settings. Anyway, changing that flag will default all websites to dark mode.
