Drop patch for template_url_service_factory.cc for chromium_src override

[mariospr]

Now that we're no longer relying on BRAVE_CHROMIUM_BUILD, we can have a
chromium_src override instead to define the Brave-specific behaviour
here, and drop this patch.

Fixes brave/brave-browser#14221

Resolves

Submitter Checklist:

• There is a ticket for my issue
• Used Github auto-closing keywords in the PR description above
• Wrote a good PR/commit description
• Added appropriate labels (QA/Yes or QA/No; release-notes/include or release-notes/exclude; OS/...) to the associated issue
• Checked the PR locally: npm run test -- brave_browser_tests, npm run test -- brave_unit_tests, npm run lint, npm run gn_check, npm run tslint
• Ran git rebase master (if needed)
• Requested a security/privacy review as needed

Reviewer Checklist:

• New files have MPL-2.0 license header
• Adequate test coverage exists to prevent regressions
• Major classes, functions and non-trivial code blocks are well-commented
• Changes in component dependencies are properly reflected in gn
• Code follows the style guide
• Test plan is specified in PR before merging

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, 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-Exceptions-in-Brave
  • https://github.com/brave/brave-browser/wiki/QA-Guide
  • https://github.com/brave/brave-browser/wiki/P3A

Test Plan:

See Test plan from #310

[mkarolin]

++

[mariospr]

Thanks, merged