fix: add lifespan context manager to StreamableHTTP mounting examples (#1669)

Co-authored-by: TheMailmans <tyler@example.com>
Co-authored-by: Marcelo Trylesinski <marcelotryle@gmail.com>

examples/snippets/servers/streamable_http_basic_mounting.py

@@ -5,6 +5,8 @@ Run from the repository root:
     uvicorn examples.snippets.servers.streamable_http_basic_mounting:app --reload
 """
 
+import contextlib
+
 from starlette.applications import Starlette
 from starlette.routing import Mount
 
@@ -20,9 +22,17 @@ def hello() -> str:
     return "Hello from MCP!"
 
 
+# Create a lifespan context manager to run the session manager
+@contextlib.asynccontextmanager
+async def lifespan(app: Starlette):
+    async with mcp.session_manager.run():
+        yield
+
+
 # Mount the StreamableHTTP server to the existing ASGI server
 app = Starlette(
     routes=[
         Mount("/", app=mcp.streamable_http_app()),
-    ]
+    ],
+    lifespan=lifespan,
 )