RequireAuthMiddleware omits RFC 6750 scope in WWW-Authenticate on 401/403

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

Summary

RequireAuthMiddleware._send_auth_error builds WWW-Authenticate with error and error_description (and optional resource_metadata), but never includes the scope parameter, even when required_scopes is configured.

This breaks RFC 6750 Section 3.1 and the MCP Authorization scope-selection / step-up flow. The SDK client already expects scope via extract_scope_from_www_auth() and uses it in get_client_metadata_scopes() as the highest-priority source when handling 403 insufficient_scope.

Actual behavior

For a server configured with required_scopes=["api.read"]:

401 (no/invalid token):

WWW-Authenticate: Bearer error="invalid_token", error_description="Authentication required"

403 (token missing required scope):

WWW-Authenticate: Bearer error="insufficient_scope", error_description="Required scope: api.read"

Neither response includes scope="api.read".

Expected behavior

When required_scopes is non-empty, the challenge should include the RFC 6750 scope parameter, e.g.:

WWW-Authenticate: Bearer error="insufficient_scope", error_description="Required scope: api.read", scope="api.read"

(and similarly for 401 when scopes are configured, so the client can request the correct scopes on initial authorization).

Impact

• MCP clients cannot reliably discover required scopes from the challenge header.
• Step-up authorization falls back to PRM scopes_supported (or omits scope), which is lower priority per the MCP scope selection strategy and can fail when PRM does not advertise scopes.
• The SDK client already implements the correct consumer side; only server emission is missing.

Root cause

In src/mcp/server/auth/middleware/bearer_auth.py, _send_auth_error builds:

www_auth_parts = [f'error="{error}"', f'error_description="{description}"']
if self.resource_metadata_url:
    www_auth_parts.append(f'resource_metadata="{self.resource_metadata_url}"')

It never appends scope= from self.required_scopes, which is already available on the middleware instance.

Present on both v1.x and main (verified in current source).

Suggested fix

When self.required_scopes is non-empty, append:

www_auth_parts.append(f'scope="{" ".join(self.required_scopes)}"')

Happy to open a PR against v1.x once a maintainer assigns this issue to me. Please also advise whether a follow-up for main (v2) is desired.

Example Code

Python & MCP Python SDK

Python: 3.14.6
MCP Python SDK: 1.28.1 (also reproduced against current v1.x / main source of RequireAuthMiddleware._send_auth_error)

從 src/mcp/server/auth/middleware/bearer_auth.py 開始，重點關注 RequireAuthMiddleware._send_auth_error 及其現有的 WWW-Authenticate 建構方式。檢查周圍的驗證回應涵蓋範圍，然後驗證已設定 required_scopes 時的 401 和 403 兩種情況；完成的標準是 challenge 暴露所需的 scope，同時保留現有參數。