Adds Fastify Middleware for v2

[andyfleming]

This adds middleware for Fastify in the same format as the other adapters/middleware (for hono and express).

Motivation and Context

This adds support for fastify as discussed in the SDK V2 Issue.

• See SDK V2 #809
• Also discussed in Fastify support or custom HTTP adapter? #441

How Has This Been Tested?

• Unit tests (equivalent to the other adapters/middleware)
• Manually tested by consuming this package with MCP server using Fastify.

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

One small difference in behavior is that this middleware uses the Fastify logger rather than console.warn like the other middleware.

[changeset-bot]

🦋 Changeset detected

Latest commit: c28b5c7

The changes in this PR will be included in the next version bump.

This PR includes changesets to release 1 package

Name	Type
@modelcontextprotocol/fastify	Minor

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commit: c28b5c7

[felixweinberger]

Rebased on main and added a changeset

[KKonstantinov]

Nit: has to be added to pkg-pr-new on the pipeline

[felixweinberger]

Thanks!