Fix #7991: Opening in private using app context menu or shortcut widget does not respect biometrics toggle

[soner-yuksel]

Summary of Changes

Adding private lock case to the external link open

This pull request fixes #7991

Submitter Checklist:

• Unit Tests are updated to cover new or changed functionality
• User-facing strings use NSLocalizableString()
• New or updated UI has been tested across:
  • Light & dark mode
  • Different size classes (iPhone, landscape, iPad)
  • Different dynamic type sizes

Test Plan:

1. Fresh profile install
2. From the homescreen, use app context menu and select New Private Tab
3. From the homescreen, add the brave shortcuts widget, use Private Tab button to open private tab

Screenshots:

RPReplay_Final1693335789.MP4

Reviewer Checklist:

• Issues include necessary QA labels:
  • QA/(Yes|No)
  • bug / enhancement
• Necessary security reviews have taken place.
• Adequate unit test coverage exists to prevent regressions.
• Adequate test plan exists for QA to validate (if applicable).
• Issue and pull request is assigned to a milestone (should happen at merge time).