[FEATURE] Support disabling claude.ai MCP connectors at the project level

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 use claude.ai MCP connectors (Slack, Linear, Google Calendar, etc.) in several of my repositories for project management workflows. But in some repos — like a product I'm building — I want a clean, focused coding environment with no cloud connectors cluttering the tool list or consuming context window.

There's currently no way to disable claude.ai MCP connectors at the project level. The only MCP-related settings in .claude/settings.json (disabledMcpjsonServers, allowedMcpServers, deniedMcpServers) control locally-configured servers from .mcp.json, not cloud connectors.

Proposed Solution

A project-scoped setting in .claude/settings.json to disable cloud MCP connectors:

{
  "cloudMcpConnectors": "disabled"
}

Or more granularly:

{
  "disabledCloudMcpConnectors": ["Slack", "Linear", "Google Calendar"]
}

This should:

• Prevent the connectors from loading in that project's sessions
• Remove them from the /mcp panel (not just block tool calls)
• Not affect other projects where the connectors are useful

Alternative Solutions

• Setting ENABLE_CLAUDEAI_MCP_SERVERS=false in .claude/settings.json under env — has no effect, connectors still appear after fresh sessions.
• Using permissions.deny: ["mcp__claude_ai_*"] — prevents tool calls but connectors still load, still appear in /mcp, and still consume context with their system instructions.

Priority

High - Significant impact on productivity

Feature Category

MCP server integration

Use Case Example

I have two repos:

1. Internal ops repo — I use Slack, Linear, and Google Calendar connectors to manage tasks and communicate with teammates directly from Claude Code.
2. Product 1 (product repo) — a focused coding project where cloud connectors are irrelevant noise. I want only my local MCP servers and no cloud connectors because this project should not push anything to my company's repos.

Today if i open (2) and type /mcp, and see 14 claude.ai connectors I don't need. Their tool definitions inflate my context window and their system instructions add noise. I want to add one setting to .claude/settings.json and have a clean environment scoped to this project only.

Additional Context

_No response_