Do all browsers support private browsing?

I use Safari 14 on a MacBook Pro. Recently, I decided to try using private windows exclusively. I really like the experience so far. Cookies, caches, and other site-specific data disappear as soon as I close the tab or window. Yes, I now need to login every time I visit a site that requires it -- no big deal, the built-in password manager in Safari makes that easy. I also lose the browsing history for that window, but if I think I will return to a website I simply create a bookmark.

Do other browsers offer the same feature?