Clean up examples (#182)

* Centralize example server transport logic in shared utils

Move stdio/HTTP transport handling into `server-utils.ts` so example
servers only need to call `startServer(createServer)`. Switch HTTP
transport to stateless mode and remove legacy SSE endpoints.

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

* Make example servers self-contained with local server-utils

Copy `server-utils.ts` into each example's `src/` directory so examples
can be used standalone without the shared directory. Updates imports
from `"../shared/server-utils.js"` to `"./src/server-utils.js"`.

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

* Add `integration-server` example for E2E testing

Add dedicated `integration-server` example (duplicated from
`basic-server-react`) to preserve E2E testing capabilities while
allowing `basic-server-react` to be simplified as a minimal example.

Changes:
- Add `examples/integration-server` exercising SDK communication APIs
- Update E2E tests to use `integration-server` instead of
  `basic-server-react` and `basic-server-vanillajs`
- Use server name labels instead of indices for more robust test
  selection
- Remove `basic-react.png` and `basic-vanillajs.png` golden snapshots

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

* Simplify `basic-server-*` examples

- Clarify comments
- Return plain text from `get-time` tool instead of JSON
- Remove simulated cleanup delay from `onteardown`

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

---------

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

examples/integration-server/tsconfig.json

@@ -0,0 +1,20 @@
+{
+  "compilerOptions": {
+    "target": "ESNext",
+    "lib": ["ESNext", "DOM", "DOM.Iterable"],
+    "module": "ESNext",
+    "moduleResolution": "bundler",
+    "allowImportingTsExtensions": true,
+    "resolveJsonModule": true,
+    "isolatedModules": true,
+    "verbatimModuleSyntax": true,
+    "noEmit": true,
+    "jsx": "react-jsx",
+    "strict": true,
+    "skipLibCheck": true,
+    "noUnusedLocals": true,
+    "noUnusedParameters": true,
+    "noFallthroughCasesInSwitch": true
+  },
+  "include": ["src", "server.ts"]
+}