Add AI task for Anthropic

[Shulyaka]

Proposed change

Add AI Task for Anthropic integration.

A note about structured output:

Although Anthropic API does not support native JSON output, several methods exist. For instance:

1. Add the JSON schema to the prompt and ask the model to respond with the requested schema, then prefill the response with '{' to skip any preamble. This method is explained in the docs here: https://docs.claude.com/en/docs/test-and-evaluate/strengthen-guardrails/increase-consistency
2. Add a new tool and have the model call this tool for the output. This method is described by Anthropic here: https://docs.claude.com/en/docs/agents-and-tools/tool-use/overview#tool-use-examples

This PR implements the second method.

Type of change

• Dependency upgrade
• Bugfix (non-breaking change which fixes an issue)
• New integration (thank you!)
• New feature (which adds functionality to an existing integration)
• Deprecation (breaking change to happen in the future)
• Breaking change (fix/feature causing existing functionality to break)
• Code quality improvements to existing code or addition of tests

Additional information

• This PR fixes or closes issue: fixes Anthropic integration does not create AI Task entity #153772
• This PR is related to issue:
• Link to documentation pull request:
• Link to developer documentation pull request:
• Link to frontend pull request:

Checklist

• I understand the code I am submitting and can explain how it works.
• The code change is tested and works locally.
• Local tests pass. Your PR cannot be merged unless tests pass
• There is no commented out code in this PR.
• I have followed the development checklist
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• The code has been formatted using Ruff (ruff format homeassistant tests)
• Tests have been added to verify that the new code works.
• Any generated code has been carefully reviewed for correctness and compliance with project standards.

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• Documentation added/updated for www.home-assistant.io

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• The manifest file has all fields filled out correctly.
  Updated and included derived files by running: python3 -m script.hassfest.
• New or updated dependencies have been added to requirements_all.txt.
  Updated by running python3 -m script.gen_requirements_all.
• For the updated dependencies - a link to the changelog, or at minimum a diff between library versions is added to the PR description.

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