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

src/mcp/shared/context.py

@@ -1,15 +1,16 @@
 from dataclasses import dataclass
-from typing import Any, Generic, TypeVar
+from typing import Generic, TypeVar
 
 from mcp.shared.session import BaseSession
 from mcp.types import RequestId, RequestParams
 
 SessionT = TypeVar("SessionT", bound=BaseSession)
+LifespanContextT = TypeVar("LifespanContextT")
 
 
 @dataclass
-class RequestContext(Generic[SessionT]):
+class RequestContext(Generic[SessionT, LifespanContextT]):
     request_id: RequestId
     meta: RequestParams.Meta | None
     session: SessionT
-    lifespan_context: Any
+    lifespan_context: LifespanContextT