Why aren't all installed browsers listed as Preferred browser options? (Brave for iOS)

I see Safari, Firefox, Firefox Focus, and Google Chrome (though Chrome doesn’t appear to be selectable; only listed)… But I also have ‘Brave’ for iOS installed and I would like to use it as my preferred browser.

Is this something that must be baked in on your end, or should I try to reinstall Brave to get it to be detected as an option?