Add webdriver test to noScript exceptions

[luixxiul]

Follow up to #8783
Closes #8837

Auditors:

Test Plan:

1. Run: BRAVE_TEST_COMMAND_LOGS=1 npm run test -- --grep='does not apply exceptions from private tabs to regular tabs'

Submitter Checklist:

• Submitted a ticket for my issue if one did not already exist.
• Used Github auto-closing keywords in the commit message.
• Added/updated tests for this change (for new code or code which already has tests).
• Ran git rebase -i to squash commits (if needed).

Reviewer Checklist:

Tests

• Adequate test coverage exists to prevent regressions
• Tests should be independent and work correctly when run indivually or as a suite ref

[bbondy]

++ thanks!