"Site search" shortcuts should work in both normal and private windows

Brave has the ability to use keywords/shortcuts in the URL bar to search on specific websites. (Right click the search bar, “Manage Search Engines and Site Search”) While the “Search engines” shortcuts like :br work in private windows, the “Site search” shortcuts do not. Google Chrome allows shortcuts in incognito windows, and I think that Brave should work similarly.

It’s a minor frustration that seems like it should be easy to fix.