MCP connection works in Claude Code but fails in Claude Web/App

## Issue Description
MCP connection is working properly in Claude Code, but suddenly stopped working in Claude Web/App interface.

## Environment
- **IDE**: IntelliJ IDEA
- **Plugin**: MCP Server Plugin (latest version)
- **Claude Interface**: Web/App (connection issue) vs Claude Code (working fine)

## Configuration Status
- ✅ `claude_desktop_config.json` is properly configured
- ✅ IntelliJ MCP Server Plugin is properly installed and configured
- ✅ MCP connection works perfectly in Claude Code
- ❌ MCP connection fails in Claude Web/App

## Expected Behavior
MCP connection should work consistently across all Claude interfaces (Code, Web, App).

## Actual Behavior
- Claude Code: MCP tools and IDE integration work as expected
- Claude Web/App: No MCP tools available, connection appears to be broken

## Additional Context
The issue started recently - it was working before but suddenly stopped working specifically in the web/app interface while continuing to work in Claude Code.

## Questions
1. Are there known differences in MCP implementation between Claude Code and Claude Web/App?
2. Is there additional configuration needed for web/app interface?
3. Could this be related to recent updates in the Claude web interface?