brave extension: remove shields blocking data for closed tabs

[petemill]

Resolves brave/brave-browser#23559

Even though we're fully removing all this code via #13638, fixing this bug might be more palatable for uplift to a release channel.

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:

[brave-builds]

A Storybook has been deployed to preview UI for the latest push

[petemill]

windows-x86 just failed at the last delta step - all build and tests seems to have passed as well as regular windows, macos, linux, etc.

[kjozwiak]

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

Brave | 1.42.42 Chromium: 103.0.5060.66 (Official Build) nightly (64-bit)
-- | --
Revision | 20b1569438a85e631d15e83eb355e3e326e5da6f-refs/branch-heads/5060@{#1066}
OS | Windows 11 Version 21H2 (Build 22000.739)

@brave/qa-team just a heads up that this one is a bit hard to reproduce but essentially you'll need to run through the following STR/Cases with an affected version and then run through the STR/Cases with a version that has the above fix.

• open a new installation of brave and open the Task manager via More tools
• open https://www.cnn.com and open another ~10 tabs by opening random links on https://www.cnn.com
• ensure that you have another Brave window opened without any tabs other than the active brave://newtab
• close the window with the ~10 CNN tabs
• restore the same window with the CNN tabs via Settings -> History -> Recently closed
• cycle through each of the tabs and then close the window with all the tabs once again
• repeat the above re: closing/re-opening and cycling through the tabs (x30-40 times)

Eventually you'll see that the Extension: Brave process via get to about ~90-100MB after doing the above for ~10-15 times or even more. However, eventually the memory will drop back to about ~30-40MBs.

Now if you repeat the same thing with version that has the above fix, the memory never gets close to ~100MB when running through the same STR/Cases outlined above.