Support safeAreaInsets + type-checking in video-resource-server

Apply host-provided safe area insets as padding on the main container,
and update `tsconfig.json` to use `moduleResolution: "bundler"` for
correct resolution of `McpUiHostContext` type with Vite.

Also adds `tsc --noEmit` to the build script to catch type errors, and
fixes pre-existing type safety issue with `blob` property access by
using proper type narrowing.

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

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

examples/video-resource-server/tsconfig.json

@@ -1,15 +1,19 @@
 {
   "compilerOptions": {
     "target": "ESNext",
-    "module": "NodeNext",
-    "moduleResolution": "NodeNext",
+    "lib": ["ESNext", "DOM", "DOM.Iterable"],
+    "module": "ESNext",
+    "moduleResolution": "bundler",
+    "allowImportingTsExtensions": true,
+    "resolveJsonModule": true,
+    "isolatedModules": true,
+    "verbatimModuleSyntax": true,
+    "noEmit": true,
     "strict": true,
     "skipLibCheck": true,
-    "esModuleInterop": true,
-    "resolveJsonModule": true,
-    "declaration": false,
-    "outDir": "dist",
-    "lib": ["ESNext", "DOM"]
+    "noUnusedLocals": true,
+    "noUnusedParameters": true,
+    "noFallthroughCasesInSwitch": true
   },
-  "include": ["server.ts", "src/**/*"]
+  "include": ["src", "server.ts"]
 }