Make browser extension setup reproducible

[jt55401]

Summary

• document the required sibling browser-client checkout and CI-pinned revision
• list the CI-equivalent validation sequence and current browser adapter status
• refresh dependency locks, including copy-webpack-plugin 14, to clear current advisories

Validation

• npm audit: 0 vulnerabilities
• npm run lint: 0 errors, 82 existing warnings
• npm test: 54 passed
• npm run typecheck
• Chromium, Firefox, and Safari builds