add API Extractor coverage for main and core exports - #2157

Summary

• add committed API Extractor reports for livekit-client and livekit-client/core
• check both reports in the smoke workflow and provide an update script for intentional API changes
• exercise Room behavior through the packaged native ESM, UMD, Vite ESM, and webpack CommonJS builds
• make the connection checker emit valid core declaration types discovered while extracting the core API

Testing

• full SDK build, worker builds, downlevel declarations, and built-import checks
• API Extractor checks for the main and core entry points
• TypeScript and core import/type boundary checks
• 24 Room-related unit tests
• 5 Playwright packaged-consumer smoke tests
• ESLint, Prettier, and Git whitespace checks

Note

API Extractor 7.59.4 currently bundles TypeScript 5.9.3, so it prints an informational warning for this repository's TypeScript 6.0.2 declarations. Both report checks pass.