I have an iPhone 14, Brave Browser (iOS) version 1.77 (99) ← but not set as the default browser for the iPhone. In my iPhone’s Brave Browser (iOS) settings:
- “Brave Search” is among the Quick-Search Engines listed - when “Brave Search” is NOT SELECTED as the preferred search engine for “Standard Tab” and “Private Tab”.
- “Brave Search” disappears from the Quick-Search Engines listed, when “Brave Search” IS SELECTED as the preferred search engine for “Standard Tab” and “Private Tab”.
DuckDuckGo is the default search engine for my Safari app. And, despite my Brave Browser (iOS) settings (I tried “this and that”) . . . when I select some words in, for example a Brave Browser window, and then use Lookup or Web Search . . . I get Safari using DuckDuckGo to perform the online search. (While you get Brave Browser DuckDuckGo to perform the online search.)
Unfortunately, Brave Search is not listed as being eligible as a default search engine - among the Safari.app settings. I suspect that is part of the problem.
I understand that there are some functions that Brave Browser (iOS) cannot do, because it is not fully approved for some Apple (eco-system) security policies, procedures, reasons, but I do not know if your issue would be, or should be, among Apple’s reasons for some boundary.
Yet I suspect, that something in the proceedings re your issue, causes the process to use the default search engine that is set for Safari. You might test that.
Info from 2022: