[Feature] Anthropic structured output with JSON output

[randombet]

Why are these changes needed?

Anthropic released new structured output APIs. https://platform.claude.com/docs/en/build-with-claude/structured-outputs

Add support as some users asked for this.

Related issue number

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Some unrelated tests failed.
https://github.com/ag2ai/ag2/actions/runs/19579226806/job/56072652113

• I've included any doc changes needed for https://docs.ag2.ai/. See https://docs.ag2.ai/latest/docs/contributor-guide/documentation/ to build and test documentation locally.
• I've added tests (if relevant) corresponding to the changes introduced in this PR.
• I've made sure all auto checks have passed.

[joggrbot]

📝 Documentation Analysis

Joggr found 1 outdated docs in the pull request.

Autofix

Joggr opened 1 pull request(s) to fix the outdated docs.

• docs: for pull #2220, fixed 1 outdated doc(s) #2222

Outdated

file	reason	confidence
website/docs/user-guide/models/anthropic.mdx	The document remains broadly accurate for basic and intermediate usage of Anthropic Claude with AG2 (config, tool use, thinking mode, API requirements), but it is not up to date on key advanced features now landed in the codebase: native structured outputs (beta API, strict tools, dual fallback modes, and associated model/version requirements). Most critically, it does not mention strict tool/response_format mode capabilities or new model requirements for those features.	55.8%

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✅ Latest commit analyzed: b2b0915 | Powered by Joggr

[codecov]

Codecov Report

❌ Patch coverage is 10.12270% with 293 lines in your changes missing coverage. Please review.

Files with missing lines	Patch %	Lines
autogen/oai/anthropic.py	10.12%	293 Missing ⚠️

Files with missing lines	Coverage Δ
autogen/oai/anthropic.py	19.50% <10.12%> (-4.66%)	⬇️

... and 19 files with indirect coverage changes

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