fix: Set the Server session initialization state immediately after respond…

[daamitt]

Set the Server session initialization state immediately after responding to InitializeRequest to fix the race condition that gives the following warnings

WARNING Failed to validate request: Received request before initialization was complete session.py:363 DEBUG Message that failed validation: method='tools/list' params={} jsonrpc='2.0' id=2 session.py:364 

Motivation and Context

For Stateful http mcp servers (when stateless_http=False) this change is required for most clients to work correctly. I have tested this with Claude desktop and VSC. Mcp Inspector does not show the issue as it does not automatically call tools/list after initialize.

This change brings the behaviour of the mcp python-sdk inline with the TS sdk
[TS SDK link] https://github.com/modelcontextprotocol/typescript-sdk/blob/caa25503cdfc449d116c204e866bccc2617d7037/src/server/streamableHttp.ts#L501

How Has This Been Tested?

A test case is attached to the PR
main.py

uv run pytest :
Results (19.93s):
633 passed
2 skipped
1 xfailed

Breaking Changes

No

Types of changes

• [ x] 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

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

Additional context

[daamitt]

Description mentions the warning msg but actually most MCP clients fail to list the prompts and tools due to this.

[maxisbey]

Thank you for the PR! I ended up writing a unit test while investigating this PR just to validate the issue and my understanding. I've pushed that up to your branch since I already had it prepared.

[daamitt]

Thank you for the test case, it captures the race condition well. The race condition is quite common when there are async awaits in the HTTP request handling - like custom middleware for auth.