[FEATURE] Support MCP prompts as "slash" commands in VS Code extension

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

Claude Code VS Code extension currently does not expose MCP Prompts (https://modelcontextprotocol.io/specification/2025-03-26/server/prompts) as "slash" commands (where as the CLI does, for example).

Proposed Solution

• List MCP Prompts as "slash" commands or otherwise triggerable from the prompt input.
• Support elicitation of required inputs for the MCP Prompt template.

Alternative Solutions

• Use the CLI instead, which has its own shortcoming (see: See also: https://github.com/anthropics/claude-code/issues/30733)

Priority

Critical - Blocking my work

Feature Category

MCP server integration

Use Case Example

1. User launches the CC VS Code extension with MCP server connected advertising one or more Prompts
2. Prompts are not listed as a "slash" command and have no visible way of being advertised to the user

Additional Context

Here is the MCP Prompts listing working in CC CLI:

https://github.com/user-attachments/assets/c6220e48-d1ea-4ccf-b2ab-2591a0c3f1db

(Note: it errors here because it does not elicit the user for required inputs)

Here is VS Code GH Copilot behavior:

https://github.com/user-attachments/assets/6078d363-7594-4f8d-acf8-6576f4da63bb