Removed Windows only DNS over HTTP work-around

[spylogsster]

Resolves brave/brave-browser#25488

Submitter Checklist:

• I confirm that no security/privacy review is needed, or that I have requested one
• There is a ticket for my issue
• Used Github auto-closing keywords in the PR description above
• Wrote a good PR/commit description
• Squashed any review feedback or "fixup" commits before merge, so that history is a record of what happened in the repo, not your PR
• 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)

Reviewer Checklist:

• A security review is not needed, or a link to one is included in the PR description
• 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:

• steps from issue

[bsclifton]

Works great 👍 Code changes look good too. Thanks! 😄

[bsclifton]

See https://github.com/brave/security/issues/1029 for security review

[srirambv]

Verification passed on

Brave	1.46.2 Chromium: 106.0.5249.40 (Official Build) nightly (64-bit)
Revision	fab1d91915d2722d6339aaa7f4e9ce44f1e9b103-refs/branch-heads/5249@{#442}
OS	Windows 11 Version 21H2 (Build 22000.1042)

• Verified steps from brave-browser#25488 (comment)
• Verified default DNS settings is retained to Use current service provider
• Encountered DNS leak so logged a follow up issue to warn users about it #25544