Add example for stateless server with JSON response

[5enxia]

Add example for stateless server with JSON response

Motivation and Context

There was no documentation on how to use it.

How Has This Been Tested?

I haven not tested due to only changes in documentation.

Breaking Changes

No

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!

[ihrpr]

The test needs to be fixed before merging:

____________________ test_docs_examples[README.md:394-408] _____________________
black failed:
  --- before
  +++ after
  @@ -398,404 +398,404 @@
   mcp = FastMCP("StatefulServer")
 
   # Stateless server (no session persistence)
   mcp = FastMCP("StatelessServer", stateless_http=True)
 
  -# Stateless server (no session persistence, no sse stream with supported client) 
  +# Stateless server (no session persistence, no sse stream with supported client)
   mcp = FastMCP("StatelessServer", stateless_http=True, json_response=True)
 
   # Run server with streamable_http transport
   mcp.run(transport="streamable-http")

                              Summary of Failures                               
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┃  File           ┃  Function       ┃  Function Line  ┃  Error Line  ┃  Error  ┃
┡━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━╇━━━━━━━━━┩
│  tests/test_e…  │  test_docs_ex…  │  [76](https://github.com/modelcontextprotocol/python-sdk/actions/runs/14996876491/job/42133173327?pr=704#step:5:77)             │              │         │
└─────────────────┴─────────────────┴─────────────────┴──────────────┴─────────┘
Results (9.18s):
         1 failed
       297 passed
         1 skipped

[5enxia]

Thank you for your review!
Sorry, I didn't know tests for docs.
I fixed it!

[ihrpr]

thank you!