perf(build): limit strict production TypeScript checks to shipped code

[yotamon]

Motivation

Production Vercel build logs show ~58 seconds spent in TypeScript checking. The root tsconfig selects 946 tracked TS/TSX files, including 147 test files and development-only scripts that don't ship in the Next.js app.

Changes

• Add tsconfig.build.json extending the existing strict tsconfig.json, excluding tests, development scripts, Firebase Functions (which have their own TypeScript compilation CI), and lint tooling.
• Give production-only type checking a separate incremental .tsbuildinfo cache to avoid collisions with local dev diagnostics.
• Configure Next.js to use the scoped config for NODE_ENV=production while preserving the full root config in development, with ignoreBuildErrors: false.
• Add regression tests checking the strict type-check gate and included/excluded paths.

Safety and verification

• No disabling of TypeScript checking. No runtime routing, static page generation, SEO or deployment settings changed.
• Existing GitHub CI should execute focused tests. Monitor next automatic production build for time reduction (no preview deployment requested).
• Full repository typechecking remains available with the existing pnpm lint / pnpm typecheck scripts.

Scope

No Vercel preview or manual release.