Always use private browsing

How does thsis option work specifically?

i gathered with the option on under "Settings >Safari" you get another option to use specific search engine of your choice, so i figured, one search engine for regular use and the other for say DuckDuckGo, yet when i swith to test in each, it always searches in Google. (Default):-

Browse the web privately in Safari on iPhone – Apple Support (AU)

1. Go to Settings  > Safari, then turn off Also Use in Private Browsing.
2. Tap Private Search Engine, then choose a search engine.

The option is not available for iPad (iOS 15.x), in my case, iPad Air 2