Add Amazon Bedrock Mantle OpenAI Responses API sample

[proton0210]

Summary

• add a self-contained introductory notebook for the OpenAI Responses API through the Amazon Bedrock bedrock-mantle endpoint
• add the mirrored website Markdown page required by the contribution guidelines
• demonstrate model discovery, non-retained requests, stored multi-turn state, retrieval, streaming, background processing, bounded polling, and actionable error handling
• document credential security, retention, project isolation, quotas, networking, observability, cost awareness, and cleanup
• add the sample to the introductory README and MkDocs navigation

Why

Amazon Bedrock supports OpenAI-compatible Models and Responses APIs through the regional Mantle endpoint, but this repository does not currently include a focused introductory sample for migrating an OpenAI Python SDK workflow to that endpoint.

The sample gives developers a single, reproducible path from secure client configuration through the major Responses API interaction modes. It does not provision AWS infrastructure.

Validation

• validated every notebook code cell as Python, excluding the expected %pip notebook magic
• verified the notebook is valid nbformat 4.5 JSON with a Python kernel, no execution counts, and no saved outputs
• tested the documented lower dependency bound, openai==1.80.0, for all SDK parameters and response helpers used by the sample
• verified all contribution-guide sections exist in both the notebook and website page
• regenerated Markdown with nbconvert and confirmed exact notebook/site content parity below the website front matter
• built the new documentation page with MkDocs in strict mode
• resolved all eight external AWS documentation links
• scanned the sample for embedded credentials and accidental use of the OpenAI production endpoint
• ran git diff --check

Live inference was not executed because it requires a contributor-specific Amazon Bedrock API key and incurs model usage charges. The notebook validates model availability at runtime and fails with actionable configuration guidance before inference when the requested model is unavailable.

Repository baseline note

The complete repository-wide MkDocs build is currently blocked by pre-existing configuration/tag validation issues outside this change, beginning with disallowed tags in docs/agents-and-function-calling/agent-code-interpreter/00_data_prep.md. The new page passes an isolated strict build and adds API-Usage-Example to the configured tag allowlist, matching the tag already used by the existing introductory API pages.

Closes #726

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