Compare redirect URIs as strings

[sp94]

Motivation and Context

When testing the simple auth example server, I encountered 400 status codes from POST /token because TokenHandler.handle was evaluating token_request.redirect_uri != authorize_request_redirect_uri as True.

This occurred because token_request.redirect_uri was of type AnyUrl, while authorize_request_redirect_uri was AnyHttpUrl, and comparing these two different Pydantic types always returns False - even if the underlying URLs are the same.

(Example: AnyUrl("http://google.com") == AnyHttpUrl("http://google.com") is False.)

I believe the example auth server worked before #895 changed some AnyHttpUrls to AnyUrls in the validation code, but the example server was not updated.

How Has This Been Tested?

Tested using Claude Code as the MCP client to connect to the example server:

claude mcp add --transport sse github http://localhost:8000/sse

The auth flow succeeded only after applying this patch.

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

We could also update the example server to declare the redirect uri as AnyHttpUrl, but I think comparing the URIs as strings would make the validation less brittle.

[sp94]

I just saw a draft PR that also addresses this: https://github.com/modelcontextprotocol/python-sdk/pull/982/files#diff-0bfdf5a468abdd078a0287db095a4ad5ebfcb04ea3e437026cdc8038c137ecab

I'll leave it to a maintainer if they want to close this or merge it in as a bug fix in the meantime