Unfortunately, DuckDuckGo is just Bing with additional privacy these days. Effectively is is what Startpage is for Google.
Brave Search is one of the only independent search indexes available these days. Others include Mojeek and Qwant, but neither are as good as Brave Search.
Hey! I wrote up a list of Open Source iOS apps on the Privacy Guides community.
I’ve been slowly trying to become platform agnostic, so I can switch back and forth between OSs without losing function. I’m not 100% there, but I hope this list helps you too if you are looking to go that route.
Copying the relevant bits here.
For iOS:
Fully FOSS:
FOSS, but with a paid tier:
Paid Only, but Open Source:
To add to this, I suggest sorting the comments by controversial on Reddit for another take.