Brave Search - Automatic Theme Not Following System Theme When In Private Mode

Description of the issue:

The default theme of the Brave Search site is “automatic”, but doesn’t follow the system theme when Brave is in Private mode. For example, the system theme is currently in “Light” or “Day” mode but the site still shows in its “Dark” or “Night” theme, making the text difficult to read. Forcing the site to display in “Light” or “Day” theme fixes the visibility issue but that then means that you have to switch to “Dark” or “Night” theme manually when the system switches its theme automatically.

Brave Version (check About Brave):
1.67 (127)

Operating System:
iOS 17.5.1