Custom search engines for New Private tabs

I recently added Brave Search as a custom search engine to the iOS app and noticed that, though I can select it as the search engine for Standard Tabs, the app does not let me select it as the search engine for Private Tabs. I assumed this was a bug, but apparently not.

So, I think it would be very useful to be able to use a custom search engine in Private Tabs. I don’t know if there is a specific rational for why this feature does not exist or if it was just never implemented, but adding it would be a good way to allow our searches in Private Tabs to be more private