Update server examples and docs

[DaleSeo]

Motivation and Context

This PR addresses outdated examples and documentation:

1. Deprecated APIs: Example files were using deprecated methods (tool, resource, prompt) instead of the current recommended APIs (registerTool, registerResource, registerPrompt)
2. Outdated protocol version: Documentation referenced protocol version 2025-03-26 instead of the latest 2025-11-25 (as defined in LATEST_PROTOCOL_VERSION)

These inconsistencies could mislead developers learning from the examples and cause them to use deprecated patterns.

How Has This Been Tested?

I ran each updated server locally and checked that they're still working like before using MCP Insepctor.

Breaking Changes

None. These changes only affect example code and documentation, not the SDK itself.

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

[pkg-pr-new]

Open in StackBlitz

npm i https://pkg.pr.new/modelcontextprotocol/typescript-sdk/@modelcontextprotocol/sdk@1285

commit: d9c9218

[felixweinberger]

Thanks!