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/customer-segmentation-server/README.md

@@ -63,4 +63,4 @@ The tool is linked to a UI resource via `_meta.ui.resourceUri`.
 - Generates realistic customer data with Gaussian clustering around segment centers
 - Each segment has characteristic ranges for revenue, employees, engagement, etc.
 - Company names generated from word-list combinations (e.g., "Apex Data Corp")
-- Data cached in memory for session consistency
+- Data cached in memory for consistency across requests