unfortunately, for some crazy reason it is hidden, like many basic features in firefox now (for example password import from file, despite export still being visible...).
Just enable browser.search.separatePrivateDefault.ui.enabled and set-up whatever you want.
I prefer to use brave in normal mode because I can select my country and get decent results, but it is useless in private mode because I would have to set-up my country every time so I just use google in private mode, where I only have to reject cookies.