Fix web search from context menu in private window(also tor)

[simonhong]

Context menu web search should use current profile's search engine url.

Fix brave/brave-browser#1758
Fix brave/brave-browser#1037

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).
• Verified that these changes build without errors on
  • Windows
  • macOS
  • Linux
• Verified that these changes pass automated tests (npm test brave_unit_tests && npm test brave_browser_tests) on
  • Windows
  • macOS
  • Linux
• Ran git rebase master (if needed).
• Ran git rebase -i to squash commits (if needed).
• Tagged reviewers and labelled the pull request as needed.
• Request a security/privacy review as needed.
• Add appropriate QA labels (QA/Yes or QA/No) to include the closed issue in milestone

Test Plan:

yarn test brave_browser_tests --filter=BraveAutocompleteProviderClientTest.DependentServiceCheckTest

Reviewer Checklist:

• New files have MPL-2.0 license header.
• Request a security/privacy review as needed.
• Adequate test coverage exists to prevent regressions
• Verify test plan is specified in PR before merging to source

[darkdh]

++