refactor: consolidate browser workbench and remove E2E infrastructure

[jikkai]

Summary

• Consolidate the browser workbench and reorganize the browser-facing examples.
• Remove the legacy E2E workflows, Playwright configuration, fixtures, visual snapshots, and E2E-only mock data package.
• Update debugger, facade, example, package, workspace, and documentation configuration to match the new structure.

Testing

• Not run locally; this PR primarily removes and reorganizes E2E infrastructure.
• CI checks should validate the updated build, lint, typecheck, and test configuration.

Checklist

• No breaking changes intentionally introduced.
• Related issue: none.

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 81.18%. Comparing base (e48e155) to head (0a6f937).

Additional details and impacted files

@@           Coverage Diff           @@
##              dev    #7600   +/-   ##
=======================================
  Coverage   81.17%   81.18%           
=======================================
  Files        2702     2702           
  Lines      169845   169858   +13     
  Branches    42030    42072   +42     
=======================================
+ Hits       137870   137897   +27     
+ Misses      31927    31913   -14     
  Partials       48       48           

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