Custom MCP Connectors return 403/Not connected in Claude Code mode but work in Claude chat mode

Summary

Custom MCP Connectors configured in Claude Desktop (Settings → Connectors) are not functional when called from Claude Code mode (the embedded CLI in Claude Desktop). The same connectors work fine in regular Claude chat mode.

Environment

• Claude Desktop (Windows 11)
• Claude Code embedded in Claude Desktop
• Two custom MCP connectors configured: https://kb.mofanai.cloud/mcp (jason-kb) and https://game-kb.mofanai.cloud/mcp (game-kb)
• Both connectors use OAuth + Streamable HTTP transport (Python MCP SDK)

Behavior

• Claude chat mode: Connectors work as expected
• Claude Code mode: All tool calls return 403 or Not connected regardless of connector auth state

What I've verified

• MCP server access logs (Caddy + Python MCP SDK): zero requests received when tool calls are made from Claude Code — the 403 originates in Anthropic's connector proxy layer, not from the server
• OAuth flow completes successfully (browser popup appears, token issued, connector shows "Connected" in UI)
• Server-side OAuth state is intact: valid access tokens present, correct issuer/resource metadata
• Anthropic support confirmed: "This appears to be an auth state synchronization issue on our side. The 403 errors happening without requests reaching your server indicate the problem is in our connector proxy layer."
• Tried: Disconnect → wait 3 min → reconnect via incognito → clear cookies → new conversation. Issue persists.
• Both connectors stopped working in Claude Code mode. Other MCP tools (non-Connector) work fine.

Expected behavior

Custom Connectors configured in Claude Desktop should be callable from Claude Code mode, same as from chat mode.

Additional context

The connectors are accessible externally and OAuth metadata is correct:

GET https://kb.mofanai.cloud/.well-known/oauth-authorization-server
→ { "issuer": "https://kb.mofanai.cloud/", ... }  ✓

Anthropic support has been contacted and a manual token reset was attempted but did not resolve the issue, suggesting this may be a broader bug affecting Claude Code's access to Connector-based MCP servers.