feat(build): enable TypeScript incremental compilation across monorepo

[Emelie-Dev]

Description

This PR tackles the slow TypeScript build times in the monorepo by enabling true incremental compilation across all packages and leveraging TypeScript project references (tsc -b).

Problem

Previously, pnpm -r build would sequentially compile all apps and packages entirely from scratch. With zero cache strategy or dependency awareness, modifying a single file could result in 30+ seconds of full workspace rebuilds, bottlenecking iteration cycles.

Solution

1. Incremental Base Configuration:
   Updated tsconfig.base.json to use incremental: true, set tsBuildInfoFile to keep the root directory clean, and enabled composite: true for downstream dependencies.
2. Project References:
   Introduced a new root tsconfig.json that hooks into all Next.js apps, TypeScript packages, and utilities using native TypeScript project references.
3. Build Script Enhancements:
   Replaced the basic builder with dependency-aware tsc -b via package.json, along with a robust build:clean utility for deep wipeouts.
4. Housekeeping:
   Added the generated .tsbuildinfo cache files to .gitignore and documented the caching mechanism in the README.md for team visibility.

Related Issue

Fixes: [Link the original issue here]

Testing and Benchmarks

• First Run: pnpm -r build or pnpm build — A full compile executes, generating .tsbuildinfo locally in each project.
• Subsequent Runs: After modifying a file, pnpm build will accurately compile only the affected references. You should see times dramatically drop from ~30s+ down to <5 seconds.

closes #337