Retire dormant hosted AI proxy

[sarthakagrawal927]

Summary

• remove the unused Vercel function and routing configuration
• retire browser cloud-provider and API-key handling
• keep AI coaching local-only through authenticated CLIs
• replace the transitive Node types dependency with a direct tooling dependency
• update durable product, deployment, architecture, and security truth

Validation

• pnpm lint
• pnpm typecheck
• pnpm build
• pnpm test
• ./scripts/docs-validate.sh
• git diff --check

Known baseline: production build retains the existing >500 kB chunk warning; cleanup audit retains unrelated dependency advisories and four Blume-related Knip findings.

Closes #6