Update routing for streamable HTTP to avoid 307 redirect

[yurikunash]

Setup the endpoint for the streamable HTTP (/mcp) in the routing table as a route served by an ASGI app, instead of mounting it as a base path.

Resolves: #732

As mentioned in MCP specification (version 2025-06-18):

The server MUST provide a single HTTP endpoint path (hereafter referred to as the MCP endpoint) that supports both POST and GET methods. For example, this could be a URL like https://example.com/mcp

This also aligns with JSON-RPC specification.

Motivation and Context

The change is required to avoid a 307 Temporary Redirect, from /mcp to /mcp/ endpoint, which currently happens. The redirect causes issues for several popular clients and also impedes hosting MCP servers behind proxy servers.

How Has This Been Tested?

Tested locally and on a remote server with MCP clients.

Breaking Changes

The users who have MCP clients configured to consume the endpoint with a slash, e.g. /mcp/, will start experiencing a 307 Temporary redirect to the endpoint without the slash /mcp.

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

[ihrpr]

Thank you!

#781 is addressing the same issue, I'll add a similar test to this PR.

[yurikunash]

Thank you for looking into the PR @ihrpr