CLI should inherit MCP tools from connected VS Code instance

Describe the feature or problem you'd like to solve

When Copilot CLI is connected to a VS Code instance that has MCP extensions installed (e.g., MSSQL Agent, Anthropic Tools, etc.), the CLI session should inherit access to those MCP tools. Currently, MCP tools available in VS Code are not accessible to CLI sub-agents or custom agents spawned via the task tool.

Proposed solution

Extend the CLI-to-VSCode connection to propagate MCP server configurations and tool availability so that:

• CLI sub-agents spawned via task tool receive MCP tools from the VS Code connection
• Custom agents (task with agent_type) can declare MCP tool dependencies and receive them from VS Code
• The CLI session inherits the full MCP toolset that VS Code has loaded

Use case / example workflow

1. Developer opens VS Code with MSSQL MCP extension installed
2. Developer opens Copilot CLI and connects it to the running VS Code instance
3. Developer asks CLI to spawn a custom MSSQL Agent sub-agent: "help me write an SQL migration"
4. Expected: MSSQL Agent has access to MSSQL MCP tools (database introspection, query execution, etc.)
5. Actual: MSSQL Agent receives no MCP tools (see #2630)

This pattern applies to any VS Code MCP extension (Teams calendar, mail, Notion databases, Azure resources, etc.).

Why this matters

• Leverages existing ecosystem: VS Code has mature MCP integrations already working well
• Unifies tool access: No need to duplicate MCP server configurations between VS Code and CLI
• Enables specialization: Allows agents to inherit capability from the IDE's MCP environment
• Reduces friction: Developers can use the same MCP tools in CLI workflows that they already have in VS Code

Related issues

• #2630 — Custom agent mcp-servers not connected in CLI sub-agent or --prompt contexts
• #2716 — Custom agents in .claude/agents/ don't receive MCP tools when spawned as sub-agents via task tool
• #4076 — Make the built-in research agent's MCP tools configurable

Additional context

The CLI now has a connection mechanism to VS Code (detected and used for model selection, environment context). This connection should be extended to include MCP tool propagation so that the CLI truly inherits the full IDE capability, not just partial settings.

まず、既存の CLI と VS Code 間の接続、およびサブエージェントとカスタムエージェント向けのタスクツールの経路を追跡します。関連する Issue #2630、#2716、#4076 を確認して、既存の MCP の制限を理解します。MCP の設定と VS Code から利用できるツールが CLI セッションと起動されたエージェントに届けば完了です。