Add first-party exception list to the correct adblock engine

[antonok-edm]

Resolves brave/brave-browser#34081

This was previously fixed in a more elegant/scalable/tested way by #19946, but that was reverted.

Since multiple other issues have come up in the meantime, I haven't had a good chance to update the original changes, but we should merge and uplift this one in the meantime.

Submitter Checklist:

• I confirm that no security/privacy review is needed and no other type of reviews are needed, or that I have requested them
• 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 wiki
  • npm run lint, npm run presubmit wiki, 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:

Visit the sites listed in the associated issue and confirm that the problematic elements are hidden in standard Shields mode.

[pes10k]

SGTM!

[kjozwiak]

Verification PASSED on Win 11 x64 using the following build(s):

Brave | 1.62.28 Chromium: 119.0.6045.105 (Official Build) nightly (64-bit)
-- | --
Revision | af1dadeae432bc6f1bed980ac4123d5b7dda6e24
OS | Windows 11 Version 22H2 (Build 22621.2506)

dailymail.co.uk

Example	Example

imdb.com

Example	Example

politico.com

Example	Example

---

Verification PASSED on Pixel 8 Pro running Android 14 using the following build(s):

Brave | 1.62.29 Chromium: 119.0.6045.105 (Official Build) canary (64-bit)
--- | ---
Revision | 722db0323f23c1aaee8a62326083bced61909279
OS | Android 14; Build/UD1A.230803.041; 34; REL

dailymail.co.uk

Example	Example

imdb.com

Example	Example

politico.com

Example	Example