[BUG] GitHub Integration Connect Button Non-Functional on Web and Desktop

Environment

• Platform (select one):
• [x] Anthropic API
• [ ] AWS Bedrock
• [ ] Google Vertex AI
• [ ] Other:
• Claude CLI version: Claude 0.12.28 (5f9bc7) 2025-07-18T21:14:50.000Z (using Claude web and Claude Desktop app)
• Operating System: macOS
• Terminal: Not applicable (UI issue)

Bug Description

The GitHub integration "Connect" button is non-functional across both Claude web (claude.ai) and Claude Desktop. Clicking the "Connect" button in Settings > Connectors in Desktop goes to the webpage, and clicking on it on the webpage does nothing - no authentication flow, no error message, no response whatsoever. This prevents users from using the official GitHub integration.

Steps to Reproduce

On Claude Web:

1. Navigate to claude.ai
2. Go to Settings > Connectors
3. Find GitHub in the list and click "Connect"
4. Nothing happens - button is unresponsive

On Claude Desktop:

1. Open Claude Desktop app
2. Click "+" button in chat interface
3. Select "Add from GitHub" or go to Settings > Connectors > "Connect"
4. Get redirected to web page with "Connect" button
5. Click "Connect" button
6. Nothing happens - button is unresponsive

Alternative attempt:

1. Go to Settings > Connectors > Browse connectors > Web
2. Only shows "Atlassian" connector
3. No GitHub connector available to install

Expected Behavior

• Clicking "Connect" should initiate GitHub OAuth authentication flow
• User should be redirected to GitHub to authorize access
• After authorization, the connector should show as "Connected"

Actual Behavior

• "Connect" button is completely unresponsive - no click event fires
• No authentication flow starts
• No error messages displayed
• Button remains in "Connect" state indefinitely
• Custom GitHub MCP (if configured manually) can fetch metadata but cannot access PRs
• After trying to use Github MPC, Claude Desktop breaks, with a message "Claude will return soon"

Additional Context

• Atlassian MCP connector is working correctly. Our custom MCP in the company is not working either and breaks the app now.
• This appears to be affecting multiple users (based on lack of GitHub connector in "Browse connectors")
• The issue affects both the web interface and desktop app
• Custom GitHub MCP shows it's partially functional, suggesting the backend might work but the UI connection mechanism is broken

Screenshots:
<img width="777" height="419" alt="Image" src="https://github.com/user-attachments/assets/67e2b8f3-3bb4-45d6-bbe4-522a615741e9" />

Related issues: This might be related to the broader MCP connection issues reported in #1611, #3193, and others.