[chat]Refactor global search chat integration with sendMessageWithWindow

[wanglam]

Description

Fix global search chatbot integration in firefox by refactoring with chatService. sendMessageWithWindow.

Changelog

• fix: global search chatbot integration in firefox

Check List

• All tests pass
  • yarn test:jest
  • yarn test:jest_integration
• New functionality includes testing.
• New functionality has been documented.
• Update CHANGELOG.md
• Commits are signed per the DCO using --signoff

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 60.77%. Comparing base (611dcfb) to head (a086559).
⚠️ Report is 2 commits behind head on main.

Additional details and impacted files

@@           Coverage Diff           @@
##             main   #10932   +/-   ##
=======================================
  Coverage   60.77%   60.77%           
=======================================
  Files        4533     4533           
  Lines      122257   122256    -1     
  Branches    20491    20491           
=======================================
+ Hits        74299    74303    +4     
+ Misses      42719    42714    -5     
  Partials     5239     5239           

Flag	Coverage Δ
Linux_1	26.57% <ø> (ø)
Linux_2	38.92% <ø> (ø)
Linux_3	39.48% <100.00%> (+<0.01%)	⬆️
Linux_4	33.74% <ø> (ø)
Windows_1	26.58% <ø> (ø)
Windows_2	38.90% <ø> (ø)
Windows_3	39.49% <100.00%> (+<0.01%)	⬆️
Windows_4	33.74% <ø> (+<0.01%)	⬆️

Flags with carried forward coverage won't be shown. Click here to find out more.

☔ View full report in Codecov by Sentry.
📢 Have feedback on the report? Share it here.

🚀 New features to boost your workflow:

• ❄️ Test Analytics: Detect flaky tests, report on failures, and find test suite problems.
• 📦 JS Bundle Analysis: Save yourself from yourself by tracking and limiting bundle sizes in JS merges.

[wanglam]

Checked failed ci group 17 not related my changes, should be safe to merge.