Add browser CI and credential storage guidance

[beefo]

Summary

• pin the browser CDN example to the current package version and add version-consistency coverage
• document the rememberMe/localStorage threat model and supported synchronous custom credential-store contract
• fix custom credential stores receiving an empty credential object during authentication
• modernize the Puppeteer browser harness and run browser tests in pull-request and publish workflows
• update CLAUDE.md with the current test, CI, distribution, and credential-persistence guidance

Testing

• npm ci
• npm test — 34 passing
• git diff --check
• validated both GitHub Actions workflow files as YAML