Transport type naming inconsistency: `streamable_http` in example vs `streamable-http` in spec and other SDKs

[jeonsoh]

Initial Checks

• I confirm that I'm using the latest version of MCP Python SDK
• I confirm that I searched for my issue in https://github.com/modelcontextprotocol/python-sdk/issues before opening this issue

Description

In the MCP specification, the transport name is defined as “Streamable HTTP”.
In the Python SDK server code (e.g., fastmcp/server.py), the string identifier is streamable-http (with a hyphen), which matches many clients.
However, in the simple-auth-client example, the identifier is written as streamable_http (with an underscore). This discrepancy can confuse developers, and some clients (e.g., Continue) only accept the hyphenated form (streamable-http).

Problem
Following the example as-is leads developers to use streamable_http, which does not work with some clients.

Expected behavior
Please align SDK/examples with one clear approach and document it explicitly:

• Option A (accept both): Allow both streamable-http and streamable_http as input (lenient parsing), but document streamable-http as the canonical form.
• Option B (unify on one): Standardize on streamable-http as the only valid transport string in examples/docs, and raise an error/warning if streamable_http is used.

This would reduce developer confusion and ensure consistency with the spec and major client expectations.

Example Code

Python & MCP Python SDK

**Environment**  
- Python: 3.13 (project requires Python >= 3.13)  
- MCP Python SDK:  
  - fastmcp 2.10.1  
  - mcp 1.10.1