[FEATURE] Allow connecting the same MCP server multiple times

Preflight Checklist

• [x] I have searched existing requests and this feature hasn't been requested yet
• [x] This is a single feature request (not multiple features)

Problem Statement

I have multiple accounts with Sentry.dev and I want to connect them all to Claude Code Web and be able to use them in different projects.

Proposed Solution

Being able to connect the same MCP server several times.

Alternative Solutions

_No response_

Priority

High - Significant impact on productivity

Feature Category

MCP server integration

Use Case Example

_No response_

Additional Context

_No response_