Fix #6577: Hide Active NTP when backgrounding the app in private mode

[kylehickinson]

Summary of Changes

This pull request fixes #6577

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:

• Enter Private Mode and make a new tab
• Verify background the app will hide the new tab page

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).