Examples for Downstream SDK Integration

[lukedev45]

Summary

Adds a top-level examples/ directory demonstrating how a downstream SDK
integrates with ionq-core through the extension API — the first runnable,
copy-pasteable examples in the repo. Closes #56.

• examples/downstream_integration.py (sync) builds an IonQClient(extension=...)
  with a ClientExtension carrying a user_agent_token, default_headers, a
  request/response EventHook, and an error_mapper that wraps APIError /
  RateLimitError into SDK-defined error types. It submits a Bell-state circuit
  to the free simulator, waits for completion via wait_for_job, and prints
  the probabilities. A short guarded block also requests a nonexistent job so the
  error_mapper is shown converting a real NotFoundError, not just wired up.
• examples/downstream_integration_async.py mirrors the flow on the async path
  with an AsyncEventHook and the asyncio endpoint variants.
• examples/README.md documents setup (pip install ionq-core,
  export IONQ_API_KEY=...) and is linked from the top-level README.md.
• Changelog entry under [Unreleased].

No changes to ionq_core/ and no new dependencies. Both scripts use only the
public API, carry SPDX headers, and use httpx with apiKey auth.

Test plan

Lint/type/compile (run in CI — no API key needed):

• uv run ruff check — passed
• uv run ruff format --check — passed
• uv run ty check examples/ — passed
• uv run python -m compileall -q examples — passed
• uv run pytest — 242 passed, 100% coverage (examples are not collected and
  don't affect the coverage gate)

Offline smoke test (no network): both modules import, the Bell-state payload
round-trips through to_dict(), and map_error correctly maps
RateLimitError → DownstreamRateLimitError and NotFoundError → DownstreamSDKError.

End-to-end against the live simulator (requires IONQ_API_KEY) was not run in
this environment:

export IONQ_API_KEY=...
python examples/downstream_integration.py
python examples/downstream_integration_async.py