Initial Checks

• I confirm that I'm using the latest version of MCP Python SDK
• I confirm that I searched for my issue in https://github.com/modelcontextprotocol/python-sdk/issues before opening this issue

Description

I was using examples/servers/simple-auth and examples/clients/simple-auth-client to learn about the mcp and oauth integration. First issue I encountered was the server giving 404 to PRM : /.well-known/oauth-protected-resource , so I added one endpoint and then when I ran the client, the client gets 400 error from auth server.

OAuthRegistrationError: Registration failed: 400 {"error":"invalid_client_metadata","error_description":"Requested scopes are not valid: http://localhost:9001/.well-known/oauth-protected-resource/mcp"}

What I believe is OAuth client registration is incorrectly using a URL (specifically the PRM discovery URL) as a scope parameter instead of using the scopes_supported field from the Protected Resource Metadata (PRM) response.

The bug appears to be in the OAuth flow where the scope is being set incorrectly. The problematic scope value http://localhost:9001/.well-known/oauth-protected-resource/mcp matches the pattern constructed in:

# Priority 2: Path-based well-known URI (if server has a path component)
if parsed.path and parsed.path != "/":
    path_based_url = urljoin(base_url, f"/.well-known/oauth-protected-resource{parsed.path}")
    urls.append(path_based_url)

As per my understanding, Expected Behavior:
According to the MCP specification and RFC 9728, the client should:

1. Discover PRM at /.well-known/oauth-protected-resource
2. Extract scopes_supported from the PRM response
3. Use those scopes (e.g., "user") in the client registration request

Reproduction Steps

1. Start the sample MCP resource server on http://localhost:9001/mcp with PRM endpoint at /.well-known/oauth-protected-resource returning:

   {
     "resource": "http://localhost:9001",
     "scopes_supported": ["user"],
     "authorization_servers": ["http://localhost:9000"]
   }

2. Start an authorization server on http://localhost:9000
3. Create an MCP client connecting to http://localhost:9001/mcp
4. The client registration fails with the error above

Example Code

Python & MCP Python SDK

1.21.1