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>

examples/basic-server-react/package.json

@@ -4,7 +4,7 @@
   "private": true,
   "type": "module",
   "scripts": {
-    "build": "cross-env INPUT=mcp-app.html vite build",
+    "build": "tsc --noEmit && cross-env INPUT=mcp-app.html vite build",
     "watch": "cross-env INPUT=mcp-app.html vite build --watch",
     "serve": "bun server.ts",
     "start": "cross-env NODE_ENV=development npm run build && npm run serve",