feat: Update API build script and TypeScript configuration

[BuckyMcYolo]

Summary by CodeRabbit

• Chores
  • Updated build configuration to enhance TypeScript declaration file generation through a refined multi-stage build process.
  • Adjusted module resolution and compilation settings for improved bundler compatibility.

[coderabbitai]

Caution

Review failed

The pull request is closed.

📝 Walkthrough

Walkthrough

The API build process shifts from single-stage (tsup with declarations) to two-stage (tsup then tsc for declarations). The API client removes a path alias mapping for the external API package and updates module/resolution settings to ESNext and Bundler, respectively.

Changes

Cohort / File(s)	Summary
API Build Configuration apps/api/package.json, apps/api/tsup.config.ts	Build script now chains tsup with tsc to emit TypeScript declarations; dts: true removed from tsup config, deferring declaration generation to the TypeScript compiler instead.
API Client Configuration packages/api-client/tsconfig.json	Added module: "ESNext" and moduleResolution: "Bundler"; removed @repo/api/* path alias mapping and the entire paths configuration block.

Estimated code review effort

🎯 2 (Simple) | ⏱️ ~10 minutes

Poem

🐰 Declarations dance in two sweet steps,
No aliases to make the paths less direct—
TSC and tsup now pirouette together,
Building bundles lighter than a feather! ✨

✨ Finishing touches

• 📝 Generate docstrings

🧪 Generate unit tests (beta)

• Create PR with unit tests
• Post copyable unit tests in a comment
• Commit unit tests in branch dev

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