Unless using Tor, websites will be able to see your IP address when you visit them, even inside a Private Window. From your IP address, sites can often guess roughly where you are — typically your city and sometimes can be much more specific. Sites will also know everything you specifically supply them, such as search terms or input fields. If you log in, the site will know you're the owner of that account. You will be logged out when you close the Private Window because Brave will throw away the cookie which keeps you logged in.
If you are using a Private Tab with Tor connectivity, Brave will route your traffic across different Tor servers in order to hide your IP address from the site you are visiting. This doesn’t ensure perfect privacy however, as there are many ways to track a user without using IP.
Although it is Brave's mission to make you hard to track online, sites can remember you by your IP address (or some other ways to recognize your device) and connect your browsing information in a Private Window with your other traffic in Brave.