Fixes includes violation from components to browser at brave_sync_profile_sync_service.cc

[AlexeyBarabash]

Resolves brave/brave-browser#12614

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
  • Android
  • iOS
  • Linux
  • macOS
  • Windows
• Verified that these changes pass automated tests (unit, browser, security tests) on
  • iOS
  • Linux
  • macOS
  • Windows
• Verified that all lint errors/warnings are resolved (npm run lint, npm run gn_check)
• Ran git rebase master (if needed).
• Ran git rebase -i to squash commits (if needed).
• Tagged reviewers and labelled the pull request as needed.
• Requested a security/privacy review as needed.
• Added appropriate QA labels (QA/Yes or QA/No) to the associated issue
• Added appropriate release note labels (release-notes/include or release-notes/exclude) to the associated issue
• Public documentation has been updated as necessary. For instance:
  • https://github.com/brave/brave-browser/wiki/Deviations-from-Chromium-(features-we-disable-or-remove)
  • https://github.com/brave/brave-browser/wiki/Proxy-redirected-URLs
  • https://github.com/brave/brave-browser/wiki/Fingerprinting-Protections
  • https://github.com/brave/brave-browser/wiki/Brave%E2%80%99s-Use-of-Referral-Codes
  • https://github.com/brave/brave-browser/wiki/Custom-Headers
  • https://github.com/brave/brave-browser/wiki/Web-compatibility-issues-with-tracking-protection
  • https://github.com/brave/brave-browser/wiki/QA-Guide

Test Plan:

N/A

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

After-merge Checklist:

• The associated issue milestone is set to the smallest version that the
  changes has landed on.
• All relevant documentation has been updated.

[AlexeyBarabash]

Linux CI run is UNSTABLE, failed

23:31:59  1 test failed:
23:31:59      SearchEngineProviderP3ATest.DefaultSearchEngineP3A (../../brave/browser/search_engines/search_engine_tracker_browsertest.cc:34)
23:31:59  null

not related to this PR

but quite interesting as I published another PR related to P3A #7016 :)

[AlexeyBarabash]

All CI are green after restarted Windows