Upgrade TypeScript and add quality checks

[coder13]

Summary

• upgrade the workspace to TypeScript 5, remove stale or duplicate type/dependency entries, and fix the stricter type/lint issues that surfaced
• reduce frontend bundle size warnings by adding shared manual chunking for the webapp and marketing site
• add first-class repo quality scripts and a GitHub Actions workflow that runs lint and typecheck on pull requests and pushes to main

Verification

• yarn lint
• yarn typecheck
• yarn build:admin
• yarn build:projector
• yarn build:webapp
• yarn build:www

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