My config: Brave 1.77.101 with Chrome 135.0.7049.115, Windows 10 Home x64 22H2
In some of the predefined search engines, Brave is adding an argument to identify it sourced the search query.
DuckDuckGo URL: https://duckduckgo.com/?q=%s&t=brave
Startpage's URL: https://www.startpage.com/do/search?q=%s&segment=startpage.brave
Since the pre-defined search engines cannot be edited, I deleted them. Then I replaced them by using the Add button to define new search engine choices, but without Brave’s tagging argument.
Brave got caught adding affiliate arguments in its URLs for some crypto service. I think they mended their ways on that sneaky trick. However, they should not be adding tags into the searches to identify they issued the search query.