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/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",