`ClientConfig` has inconsistent naming: `message_handler` should be `message_callback`

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

ClientConfig exposes five user-facing callback fields, but four of them use the *_callback suffix while one uses *_handler:

# src/mcp/client/client.py
sampling_callback: SamplingFnT | None = None
list_roots_callback: ListRootsFnT | None = None
logging_callback: LoggingFnT | None = None
elicitation_callback: ElicitationFnT | None = None
message_handler: MessageHandlerFnT | None = None  # ← inconsistent

The same inconsistency is present in ClientSession.__init__ and ServerConnectionParams:

# src/mcp/client/session.py
def __init__(self, ..., message_handler: MessageHandlerFnT | None = None, ...)

# src/mcp/client/session_group.py
class ServerConnectionParams:
    message_handler: MessageHandlerFnT | None = None

A TODO comment in the codebase already flags this:

# TODO(Marcelo): Why do we have both "callback" and "handler"?
message_handler: MessageHandlerFnT | None = None

Proposed Fix

Rename message_handler → message_callback consistently across all three sites:

Since this is the v2 rewrite on main, a breaking rename is appropriate and there is no need for a deprecation shim.

I'd like to take this on if you're open to a fix.

Python & MCP Python SDK

Python 3.13
Reproduced on: main @ 161834d (2026-05-13)

Start with the callback definitions and forwarding calls in src/mcp/client/client.py, then follow the related parameter and internal attribute in src/mcp/client/session.py. Check ServerConnectionParams in src/mcp/client/session_group.py and the local variable and keyword argument in src/mcp/client/main.py. Done means all four sites consistently use message_callback, with no remaining message_handler naming in this flow.