Fix incorrect word count for sync

[fuchenshi]

This PR fixes the incorrect word count that the user may see when viewing or entering the sync code when setting up sync.

Before:

Screen.Recording.2025-02-01.at.08.55.28.mov

After:

Screen.Recording.2025-02-01.at.08.56.40.mov

Resolves brave/brave-browser#43635

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 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/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 brave/brave-browser#43635

[fuchenshi]

I did a force push to replace the commit with one that has a signature.

[AlexeyBarabash]

PR looks good
thanks @fuchenshi for the contributing

CI runs at #27558

[AlexeyBarabash]

CI run #27558 is green

[AlexeyBarabash]

It needs to be uplifted to beta and stable.

[bsclifton]

Admin merging. Nice work @fuchenshi! ❤️

[brave-builds]

Released in v1.77.26

[kjozwiak]

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

Brave | 1.77.26 Chromium: 133.0.6943.54 (Official Build) nightly (64-bit)
-- | --
Revision | b659cfb092f8c82ea07dad4b7f4f38b6193bf49f
OS | Windows 11 Version 24H2 (Build 26100.2894)

Using the STR/Cases outlined via #27450 (comment) & brave/brave-browser#43635 (comment), ensured that the Word count was working as expected as per the following:

Ensuring that the correct Word count is being displayed via Sync Chain Code

Previous/Updated Profile	New Profile

Ensuring that the correct Word count is being when entering Sync Chain Code manually

Recording.2025-02-09.213616.mp4