docs: document stateless Responses API

[PierreLeGuen]

Summary

• add a complete guide for stateless POST /v1/responses, caller-managed history, and client-managed custom functions
• remove Files, Conversations, response-history, and built-in Responses tool guidance from the hand-authored docs
• update the generated API Reference to the exact public contract implemented by feat(api): restrict stateful APIs for migration cloud-api#943
• keep Chat Completions web search documented as a separate supported flow

Dependency

This PR documents the contract in nearai/cloud-api#934 and nearai/cloud-api#943. It should merge with or after that API contract is deployed. It does not claim that historical data has been deleted, and it does not cover the separate data export, retention, Private Chat, or /mcp workstreams.

The generated OpenAPI change applies only the #943 delta to the currently published spec: 20 retiring operations are removed and no unrelated operations are added.

Validation

• npx --yes mint validate
• npx --yes mint broken-links
• git diff --check
• structural OpenAPI assertions: only POST /v1/responses remains; Conversations, Files, and response-history paths are absent; store defaults to false; stateful fields and built-in tools are absent from the request schema
• public-disclosure review: no private links, customer identities, usage data, or internal operational evidence

[chatgpt-codex-connector]

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