Brave on iPhone and iPad supports adding a custom search engine for standard tabs.

1. Open Brave and tap the menu.
2. Tap Settings, then Search Engines.
3. Tap Add Custom Search Engine.
4. Set the title to Queye and the URL to https://queye.co/search?s=%s.
5. Save it, then set Queye as the default for Standard Tab.

Brave's iOS support notes that custom engines cannot be used as the private-tab default.