refactor: improve lifespan context typing and documentation

- Add proper generic parameter for lifespan context type
- Update README with TypedDict example for strong typing
- Fix context variable initialization in server
- Improve property return type safety
- Remove redundant documentation
- Ensure compatibility with existing tests

README.md

@@ -128,6 +128,9 @@ The [Model Context Protocol (MCP)](https://modelcontextprotocol.io) lets you bui
 The FastMCP server is your core interface to the MCP protocol. It handles connection management, protocol compliance, and message routing:
 
 ```python
+# Add lifespan support for startup/shutdown with strong typing
+from dataclasses import dataclass
+from typing import AsyncIterator
 from mcp.server.fastmcp import FastMCP
 
 # Create a named server
@@ -136,14 +139,17 @@ mcp = FastMCP("My App")
 # Specify dependencies for deployment and development
 mcp = FastMCP("My App", dependencies=["pandas", "numpy"])
 
-# Add lifespan support for startup/shutdown
+@dataclass
+class AppContext:
+    db: Database  # Replace with your actual DB type
+
 @asynccontextmanager
-async def app_lifespan(server: FastMCP) -> AsyncIterator[dict]:
-    """Manage application lifecycle"""
+async def app_lifespan(server: FastMCP) -> AsyncIterator[AppContext]:
+    """Manage application lifecycle with type-safe context"""
     try:
         # Initialize on startup
         await db.connect()
-        yield {"db": db}
+        yield AppContext(db=db)
     finally:
         # Cleanup on shutdown
         await db.disconnect()
@@ -151,7 +157,7 @@ async def app_lifespan(server: FastMCP) -> AsyncIterator[dict]:
 # Pass lifespan to server
 mcp = FastMCP("My App", lifespan=app_lifespan)
 
-# Access lifespan context in tools
+# Access type-safe lifespan context in tools
 @mcp.tool()
 def query_db(ctx: Context) -> str:
     """Tool that uses initialized resources"""
@@ -387,7 +393,6 @@ async def query_db(name: str, arguments: dict) -> list:
 The lifespan API provides:
 - A way to initialize resources when the server starts and clean them up when it stops
 - Access to initialized resources through the request context in handlers
-- Support for both low-level Server and FastMCP classes
 - Type-safe context passing between lifespan and request handlers
 
 ```python