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.

🤖 Generated with [Claude Code](https://claude.com/claude-code)

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.

🤖 Generated with [Claude Code](https://claude.com/claude-code)

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()`.

🤖 Generated with [Claude Code](https://claude.com/claude-code)

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`

🤖 Generated with [Claude Code](https://claude.com/claude-code)

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.

🤖 Generated with [Claude Code](https://claude.com/claude-code)

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

---------

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

package-lock.json

@@ -494,6 +494,7 @@
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       "dev": true,
       "license": "MIT",
+      "peer": true,
       "dependencies": {
         "@babel/code-frame": "^7.27.1",
         "@babel/generator": "^7.28.5",
@@ -2099,6 +2100,7 @@
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       "dev": true,
       "license": "MIT",
+      "peer": true,
       "dependencies": {
         "undici-types": "~7.16.0"
       }
@@ -2123,6 +2125,7 @@
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       "dev": true,
       "license": "MIT",
+      "peer": true,
       "dependencies": {
         "csstype": "^3.2.2"
       }
@@ -2623,6 +2626,7 @@
         }
       ],
       "license": "MIT",
+      "peer": true,
       "dependencies": {
         "baseline-browser-mapping": "^2.9.0",
         "caniuse-lite": "^1.0.30001759",
@@ -3338,6 +3342,7 @@
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       "dev": true,
       "license": "ISC",
+      "peer": true,
       "engines": {
         "node": ">=12"
       }
@@ -3785,6 +3790,7 @@
       "resolved": "https://registry.npmjs.org/express/-/express-5.2.1.tgz",
       "integrity": "sha512-hIS4idWWai69NezIdRt2xFVofaF4j+6INOpJlVOLDO8zXGpUVEVzIYk12UUi2JzjEzWL3IOAxcTubgz9Po0yXw==",
       "license": "MIT",
+      "peer": true,
       "dependencies": {
         "accepts": "^2.0.0",
         "body-parser": "^2.2.1",
@@ -5316,6 +5322,7 @@
       "resolved": "https://registry.npmjs.org/react/-/react-19.2.1.tgz",
       "integrity": "sha512-DGrYcCWK7tvYMnWh79yrPHt+vdx9tY+1gPZa7nJQtO/p8bLTDaHp4dzwEhQB7pZ4Xe3ok4XKuEPrVuc+wlpkmw==",
       "license": "MIT",
+      "peer": true,
       "engines": {
         "node": ">=0.10.0"
       }
@@ -5414,6 +5421,7 @@
       "integrity": "sha512-w8GmOxZfBmKknvdXU1sdM9NHcoQejwF/4mNgj2JuEEdRaHwwF12K7e9eXn1nLZ07ad+du76mkVsyeb2rKGllsA==",
       "dev": true,
       "license": "MIT",
+      "peer": true,
       "dependencies": {
         "@types/estree": "1.0.8"
       },
@@ -6184,6 +6192,7 @@
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       "dev": true,
       "license": "MIT",
+      "peer": true,
       "engines": {
         "node": ">=12"
       },
@@ -6933,6 +6942,7 @@
       "integrity": "sha512-jl1vZzPDinLr9eUt3J/t7V6FgNEw9QjvBPdysz9KfQDD41fQrC2Y4vKQdiaUpFT4bXlb1RHhLpp8wtm6M5TgSw==",
       "dev": true,
       "license": "Apache-2.0",
+      "peer": true,
       "bin": {
         "tsc": "bin/tsc",
         "tsserver": "bin/tsserver"
@@ -7026,6 +7036,7 @@
       "integrity": "sha512-+Oxm7q9hDoLMyJOYfUYBuHQo+dkAloi33apOPP56pzj+vsdJDzr+j1NISE5pyaAuKL4A3UD34qd0lx5+kfKp2g==",
       "dev": true,
       "license": "MIT",
+      "peer": true,
       "dependencies": {
         "esbuild": "^0.25.0",
         "fdir": "^6.4.4",
@@ -7159,6 +7170,7 @@
       "integrity": "sha512-5gTmgEY/sqK6gFXLIsQNH19lWb4ebPDLA4SdLP7dsWkIXHWlG66oPuVvXSGFPppYZz8ZDZq0dYYrbHfBCVUb1Q==",
       "dev": true,
       "license": "MIT",
+      "peer": true,
       "engines": {
         "node": ">=12"
       },
@@ -7411,6 +7423,7 @@
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       "dev": true,
       "license": "ISC",
+      "peer": true,
       "bin": {
         "yaml": "bin.mjs"
       },
@@ -7455,6 +7468,7 @@
       "resolved": "https://registry.npmjs.org/zod/-/zod-4.2.1.tgz",
       "integrity": "sha512-0wZ1IRqGGhMP76gLqz8EyfBXKk0J2qo2+H3fi4mcUP/KtTocoX08nmIAHl1Z2kJIZbZee8KOpBCSNPRgauucjw==",
       "license": "MIT",
+      "peer": true,
       "funding": {
         "url": "https://github.com/sponsors/colinhacks"
       }