find_context_parameter() fails to detect Context parameter in callable class instances

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

When registering a callable class instance as an MCP tool via FastMCP.add_tool(), the ctx: Context parameter is incorrectly exposed as an externally visible tool parameter instead of being injected by the framework. This is because find_context_parameter() uses typing.get_type_hints() which doesn't introspect the call method of callable class instances.

Suggested Fix
Update find_context_parameter() to handle callable class instances:

def find_context_parameter(fn: Callable[..., Any]) -> str | None:
    from mcp.server.fastmcp.server import Context

    # Handle callable class instances by using __call__ method
    target = fn
    if not (inspect.isfunction(fn) or inspect.ismethod(fn)):
        if callable(fn) and hasattr(fn, "__call__"):
            target = fn.__call__

    try:
        hints = typing.get_type_hints(target)
    except Exception:
        return None

    # ... rest of function unchanged

Example Code

from typing import Annotated, Any
from mcp.server.fastmcp import Context, FastMCP
from mcp.server.session import ServerSession
from starlette.requests import Request
import pydantic

class MyTool:
    def __init__(self, name: str):
        self.__name__ = name

    async def __call__(
        self,
        query: Annotated[str, pydantic.Field(description="Search query")],
        ctx: Context[ServerSession, Any, Request],
    ) -> str:
        """Performs a search."""
        return f"Results for: {query}"

mcp = FastMCP(name="Test Server")
mcp.add_tool(MyTool(name="my_search"), name="my_search", description="Search tool")

# When listing tools, 'ctx' appears as a required parameter in the schema

Python & MCP Python SDK

1.26.0

Start at find_context_parameter(), which is used while registering tools through FastMCP.add_tool(). Compare its handling of regular functions with callable class instances and verify the example no longer exposes ctx as a tool parameter when the callable instance is registered.