Python: Correct ChatKit guide streaming arguments

[LI (ktz03)]

Motivation & Context

The ChatKit package agent guide passes an Agent and a message list to stream_agent_response. The helper instead accepts a stream of AgentResponseUpdate objects and a ChatKit thread ID, so the documented call raises TypeError before any model/client call.

Description & Review Guide

• What are the major changes? Obtain agent.run(messages, stream=True) first, then pass that response stream and thread_id to the ChatKit helper.
• What is the impact of these changes? Documentation only, matching the working package README call pattern. The old Usage block fails before invoking the client; the corrected block and unchanged README pattern both complete with a deterministic local client on Windows/CPython 3.14.3 and cached openai-chatkit 1.6.5. No service, frontend, HTTP request, real model, storage recovery, package build, full suite, fresh install or minimum-version matrix was exercised.
• What do you want reviewers to focus on? The helper receives its documented response-stream and thread-ID arguments. The package README and runtime implementation are unchanged.

Related Issue

N/A - trivial change. This corrects an unambiguous example call to the existing API, matching the package README; no behavior, API or new guidance principle is introduced. The original integration and guide authors in #1273, #2174 and #3644 retain their contributions.

AI Assistance

• No material AI assistance was used.
• This is an AI-assisted contribution. I reviewed, understood, and verified all submitted content and accept responsibility for it.

AI assistance details: Documentation, example verification, and this PR description.

Contribution Checklist

• The code builds clean without any errors or warnings
• All unit tests pass, and I have added new tests where possible
• The PR follows the Contribution Guidelines
• This PR links to an agreed issue with no competing open PR, or the Related Issue section documents a trivial-change or repository-automation exception.
• This is not a breaking change. If it is a breaking change, add the breaking change label (or add "[BREAKING]" to the title prefix, before or after any language prefix) — a workflow keeps the label and title prefix in sync automatically.

[Copilot]

🟢 Approval recommended

The documentation-only correction matches the existing API contract, with no unresolved findings.

No open issues 🎉

What changed in this PR

Corrects the Python ChatKit guide’s streaming example to match the existing helper API and package README.

Changes:

• Creates a response stream with agent.run(messages, stream=True).
• Passes that stream and thread_id to stream_agent_response.

File	Description
python/​packages/​chatkit/​AGENTS.md	Corrects streaming arguments in the usage example.

_{Review effort: Balanced}