docs: clarify streamable_http_path configuration when mounting servers

- Add StreamableHTTP servers section mirroring SSE servers structure
- Start with simple mounting examples, then explain path composition
- Document how to configure streamable_http_path for different scenarios
- Add inline comments in Starlette mounting example

This addresses confusion around endpoint paths when mounting
FastMCP servers as sub-applications in ASGI frameworks.

Author: felixweinberger

README.md

@@ -979,6 +979,11 @@ app = Starlette(
     ],
     lifespan=lifespan,
 )
+
+# Note: Clients connect to http://localhost:8000/echo/mcp and http://localhost:8000/math/mcp
+# To mount at the root of each path (e.g., /echo instead of /echo/mcp):
+# echo_mcp.settings.streamable_http_path = "/"
+# math_mcp.settings.streamable_http_path = "/"
 ```
 
 _Full example: [examples/snippets/servers/streamable_starlette_mount.py](https://github.com/modelcontextprotocol/python-sdk/blob/main/examples/snippets/servers/streamable_starlette_mount.py)_
@@ -1002,6 +1007,57 @@ By default, SSE servers are mounted at `/sse` and Streamable HTTP servers are mo
 
 For more information on mounting applications in Starlette, see the [Starlette documentation](https://www.starlette.io/routing/#submounting-routes).
 
+#### StreamableHTTP servers
+
+You can mount the StreamableHTTP server to an existing ASGI server using the `streamable_http_app` method. This allows you to integrate the StreamableHTTP server with other ASGI applications.
+
+```python
+from starlette.applications import Starlette
+from starlette.routing import Mount, Host
+from mcp.server.fastmcp import FastMCP
+
+
+mcp = FastMCP("My App")
+
+# Mount the StreamableHTTP server to the existing ASGI server
+app = Starlette(
+    routes=[
+        Mount('/', app=mcp.streamable_http_app()),
+    ]
+)
+
+# or dynamically mount as host
+app.router.routes.append(Host('mcp.acme.corp', app=mcp.streamable_http_app()))
+```
+
+When mounting StreamableHTTP servers, be aware that the server's `streamable_http_path` setting (default: `/mcp`) is relative to where you mount the app. For example:
+
+```python
+from starlette.applications import Starlette
+from starlette.routing import Mount
+from mcp.server.fastmcp import FastMCP
+
+# Create multiple MCP servers
+api_mcp = FastMCP("API Server")
+chat_mcp = FastMCP("Chat Server")
+
+# Default behavior: endpoints will be at /api/mcp and /chat/mcp
+app = Starlette(
+    routes=[
+        Mount("/api", app=api_mcp.streamable_http_app()),
+        Mount("/chat", app=chat_mcp.streamable_http_app()),
+    ]
+)
+
+# To mount at the root of each path (e.g., /api instead of /api/mcp):
+# Configure streamable_http_path before mounting
+api_mcp.settings.streamable_http_path = "/"
+chat_mcp.settings.streamable_http_path = "/"
+
+# Or configure during initialization
+mcp_at_root = FastMCP("My Server", streamable_http_path="/")
+```
+
 #### SSE servers
 
 > **Note**: SSE transport is being superseded by [Streamable HTTP transport](https://modelcontextprotocol.io/specification/2025-03-26/basic/transports#streamable-http).