Add support for MCP `notifications/prompts/list_changed` notifications

Description

Claude Code currently doesn't respond to notifications/prompts/list_changed notifications sent by MCP servers. This prevents dynamic prompt updates from appearing in the UI without restarting Claude Code.

Current Behavior

When an MCP server:

1. Advertises prompts.listChanged: true capability
2. Detects changes to prompt files
3. Sends notifications/prompts/list_changed notification

Claude Code does not:

• Refresh the prompt list
• Update prompt descriptions
• Show newly added prompts
• Remove deleted prompts

Expected Behavior

When receiving a notifications/prompts/list_changed notification, Claude Code should:

1. Re-fetch the prompt list from the server
2. Update the UI to reflect changes
3. Show new prompts without requiring a restart

Technical Details

MCP servers can advertise support for dynamic prompt updates:

const server = new Server(
  { name: 'my-server', version: '1.0.0' },
  {
    capabilities: {
      prompts: {
        listChanged: true,  // Indicates support for notifications
      },
    },
  },
);

// When prompts change, server sends:
await server.notification({
  method: 'notifications/prompts/list_changed',
  params: {},
});

Use Case

This feature enables:

• Hot-reloading of prompt templates during development
• Dynamic prompt loading based on context
• Better developer experience when creating/modifying prompts
• Plugin systems where prompts can be added at runtime

Additional Context

• The MCP specification includes this capability
• Other MCP clients (e.g., GitHub Copilot) support these notifications
• Similar notifications exist for tools (notifications/tools/list_changed) and resources

Related

• MCP Specification - Prompts
• Similar feature exists for resources and tools in the spec