[BUG] Custom MCP isn't connecting even after OAuth ClaudeDesktop

Preflight Checklist

• [x] I have searched existing issues and this hasn't been reported yet
• [x] This is a single bug report (please file separate reports for different bugs)
• [x] I am using the latest version of Claude Code

What's Wrong?

I have been using a custom MCP that has been working fine for the past 4 months, but a few hours ago, it stopped working. When I click configure & complete the OAuth flow, it says connected but in the notification, it says connected but Claude Web doesn't connect & still shows connect.
I validated that OAuth completed successfully on the GCP server but ClaudeDesktop doesn't connect it & updates the UI though it gives notification its connected.

<img width="681" height="155" alt="Image" src="https://github.com/user-attachments/assets/3d4d60bc-c8ce-4182-bf8e-0c60613d8511" />

<img width="911" height="769" alt="Image" src="https://github.com/user-attachments/assets/a2f967f2-2fdd-41a0-9e53-c0e4c77d3b9f" />

What Should Happen?

On Clicking on Connect button in front of custom connector it must connect successfully

Error Messages/Logs

Steps to Reproduce

1. Create a MCP Server
2. Deploy it on Cloud Run
3. Create a Custom Connector in Claude Desktop
4. Click on Connect button

Claude Model

None

Is this a regression?

Yes, this worked in a previous version

Last Working Version

_No response_

Claude Code Version

Claude Desktop

Platform

Anthropic API

Operating System

Windows

Terminal/Shell

PowerShell

Additional Information

_No response_