on ios:

brave has an app and search.brave.com site

duckduckgo has an app, might not recommend the site though (lol) but searx has a list of instances like searx.org might be their main site

so apps: maybe brave or duckduckgo, sites maybe search.brave.com or searx.org

haven't checked ios apps in a while

if you want a phone that is more pro-privacy, there's a linuxphones community on here, you want a phone that you can put a "custom rom" on probably (would be an android phone to start before you put more software on it, likely)