Fix build errors in examples (#180)

* Update `package.json`

* Add TypeScript type checking to example build scripts

Add `tsc --noEmit &&` before `vite build` in all example `package.json`
files to catch type errors during builds. Previously, type errors
in `server.ts` files were not detected because Vite/Bun transpile
without type checking.

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Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>

* Make `_meta` optional in `McpUiAppResourceConfig`

The `_meta` and `ui` properties were required, causing TypeScript errors
when calling `registerAppResource()` without providing metadata.

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Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>

* Fix Zod type compatibility in `registerAppTool()`

Use `ZodRawShapeCompat | AnySchema` from SDK's `zod-compat` module
instead of raw `ZodRawShape` to resolve type errors when examples
pass `ZodObject` schemas to `registerAppTool()`.

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Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>

* Remove unused imports in example apps

- `basic-server-react`: Remove unused `McpUiResourceTeardownResult`
- `customer-segmentation-server`: Remove unused `PostMessageTransport`

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Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>

* Fix CI git install test for fork PRs

Use `github.event.pull_request.head.repo.full_name` to correctly
reference the fork repository when testing git installs from PRs.

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Co-Authored-By: Claude <noreply@anthropic.com>

---------

Co-authored-by: Claude Opus 4.5 <noreply@anthropic.com>

.github/workflows/ci.yml

@@ -144,7 +144,7 @@ jobs:
           mkdir test-project
           cd test-project
           npm init -y
-          # Install from the PR branch
-          npm install "git+https://github.com/${{ github.repository }}#${{ github.head_ref || github.ref_name }}"
+          # Install from the PR branch (use head repo for fork PRs)
+          npm install "git+https://github.com/${{ github.event.pull_request.head.repo.full_name || github.repository }}#${{ github.head_ref || github.ref_name }}"
           # Verify the package is usable (ESM import)
           node --input-type=module -e "import { App } from '@modelcontextprotocol/ext-apps'; console.log('Import successful:', typeof App)"