Using a OnePlus 2 running OxygenOS 3.6.1 with Brave 1.5.8, the latest versions at this time, when I select to use a private tab it just opens a regular tab. This first happened a couple months ago and I fixed it by reinstalling. It didn’t take long to revert back to malfunctioning, where it has been now for a few weeks at least. To compare, this does not and has never happened in Chrome. Dreadfully, I’m going to try and reinstall again to see if it fixes for good this time but I don’t expect it to.
I don’t know how anyone else can reproduce this issue because I’ve done a fair amount of searching and was unable to find evidence anyone else has reported it.