Description of the issue:
Once you’ve created a custom search engine definition, you can make it the default for normal windows. And once you’ve done that, your custom search will be offered as a choice in the “Modify” modal for private windows. And when you select it and click on “Set as default”, a brief pop-up says that it is now the default, but the change isn’t actually made; it is immediately discarded.
How can this issue be reproduced?
Create a custom search definition and give it a unique label that can’t be confused with any of the pre-installed ones.
Go to brave://settings/search, or navigate to Settings | Search engine | Manage search engines and site search
Under “Site search”, click on “Add”.
Fill-in all three fields and click on “Add”.
In the three-dot menu of the newly created search definition, click on “Make default”.
Go back (up) one level to brave://settings/search.
In the “Private window” section, click on “Change”.Your custom search definition will be one of the options: select it and click on “Set as default”. A pop-up will briefly show “_____ is now your default search engine for private windows.” (Which seems to confirm the intent behind the option.)
Notice that the search engine that is set in the “Private Window” section is not your custom one.
Expected result:
Custom search engine definition should be retained as default for private windows.
Until this is fixed, the least annoying workaround is probably the search keyword. If your custom engine has a short keyword, you can type that keyword plus a space in the address bar in a private window and Brave should still route that single search through the custom engine. Not the same as a default, but it avoids changing the normal-window default just for private searches.