Rebuild the docs around tested examples; shrink README.v2.md to a pitch (#2978)

docs_src/asgi/tutorial003.py

@@ -0,0 +1,39 @@
+from collections.abc import AsyncIterator
+from contextlib import AsyncExitStack, asynccontextmanager
+
+from starlette.applications import Starlette
+from starlette.routing import Mount
+
+from mcp.server import MCPServer
+
+notes = MCPServer("Notes")
+tasks = MCPServer("Tasks")
+
+
+@notes.tool()
+def add_note(text: str) -> str:
+    """Save a note."""
+    return f"Saved: {text}"
+
+
+@tasks.tool()
+def add_task(title: str) -> str:
+    """Create a task."""
+    return f"Created: {title}"
+
+
+@asynccontextmanager
+async def lifespan(app: Starlette) -> AsyncIterator[None]:
+    async with AsyncExitStack() as stack:
+        await stack.enter_async_context(notes.session_manager.run())
+        await stack.enter_async_context(tasks.session_manager.run())
+        yield
+
+
+app = Starlette(
+    routes=[
+        Mount("/notes", app=notes.streamable_http_app()),
+        Mount("/tasks", app=tasks.streamable_http_app()),
+    ],
+    lifespan=lifespan,
+)