Private Window stores previous web sites

Yes. My routine is to use the private window most of the working day. At the end of the day
I shut down Brave private window and Brave non-private window and then shut down my
computer i.e. I turn the computer off. The next day I can open a private window before opening
anything else and begin typing a web site I visited the previous day or even sites I have not
visited for weeks or months before and get autofilled or a list of suggested sites I have previously
visited. I have put up with it for a long time but I am annoyed that private window does not
work as advertised.

Here is a screen shot when I type the letter i in the search box. The first site I visited today in
the private window. The DeepL and the aggienetwork sites I visited today in the non-private window.
The bottom iq site I visited yesterday. The World War I sites and the hard water site I visited last year
and have not returned to them in either the private window or the non-private. Where is are these sites being stored?