ci: add Claude GitHub Actions for @claude mentions and code review

[felixweinberger]

Adds two GitHub Actions workflows, mirroring python-sdk PR modelcontextprotocol/python-sdk#1922.

Motivation and Context

Enables @claude mentions on issues/PRs and automated code review for incoming PRs.

How Has This Been Tested?

Workflow syntax validated. Same configuration is running on python-sdk.

Breaking Changes

None.

Types of changes

• Bug fix (non-breaking change which fixes an issue)
• New feature (non-breaking change which adds functionality)
• Breaking change (fix or feature that would cause existing functionality to change)
• Documentation update

Checklist

• I have read the MCP Documentation
• My code follows the repository's style guidelines
• New and existing tests pass locally
• I have added appropriate error handling
• I have added or updated documentation as needed

Additional context

Prerequisites: Claude Code GitHub App must be installed on the repo and ANTHROPIC_API_KEY must be set as a repository secret.

Includes guards to skip fork PRs (no secrets/OIDC access) and Dependabot PRs.

[changeset-bot]

⚠️ No Changeset found

Latest commit: 9dfa382

Merging this PR will not cause a version bump for any packages. If these changes should not result in a new version, you're good to go. If these changes should result in a version bump, you need to add a changeset.

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[pkg-pr-new]

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@modelcontextprotocol/client

npm i https://pkg.pr.new/modelcontextprotocol/typescript-sdk/@modelcontextprotocol/client@1481

@modelcontextprotocol/server

npm i https://pkg.pr.new/modelcontextprotocol/typescript-sdk/@modelcontextprotocol/server@1481

@modelcontextprotocol/express

npm i https://pkg.pr.new/modelcontextprotocol/typescript-sdk/@modelcontextprotocol/express@1481

@modelcontextprotocol/hono

npm i https://pkg.pr.new/modelcontextprotocol/typescript-sdk/@modelcontextprotocol/hono@1481

@modelcontextprotocol/node

npm i https://pkg.pr.new/modelcontextprotocol/typescript-sdk/@modelcontextprotocol/node@1481

commit: 9dfa382