[FEATURE] Allow VS Code commands to accept a `prompt` parameter for extension-to-extension integration

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

Currently, there's no reliable way to programmatically send a prompt to Claude Code from another extension.

What I tried:

• vscode.commands.executeCommand('claude-vscode.sidebar.open') - opens the sidebar but accepts no prompt parameter
• vscode://anthropic.claude-code/open?prompt=... - pre-fills the prompt but always opens a new tab (not the sidebar), and doesn't submit
• Clipboard workaround - copies the prompt and tells the user to paste. Works, but poor UX

Proposed Solution

Add an optional prompt parameter to claude-vscode.sidebar.open (and other open commands):

// From another VS Code extension:
await vscode.commands.executeCommand('claude-vscode.sidebar.open', {
  prompt: 'Implement the auth module...',
});

### Alternative Solutions

Alternative would be using an URI option and add the sidebar instead of new tab.
vscode://anthropic.claude-code/open?prompt=..&location=sidebar

### Priority

High - Significant impact on productivity

### Feature Category

Developer tools/SDK

### Use Case Example

I'm building a VS Code extension ([TaskPlanner](https://marketplace.visualstudio.com/items?itemName=refined.taskplanner)) that generates task implementation prompts and dispatches them to Claude Code. 
When a user clicks "Implement with AI" on a task, the extension composes a detailed
prompt including the task description, priority, tags, and workflow steps, then needs
to hand it off to Claude Code.

### Additional Context

Cursor added this capability in v2.3 (January 2026) after a
[community request](https://forum.cursor.com/t/a-command-for-passing-a-prompt-to-the-chat/138049).
VS Code's built-in Copilot Chat also supports it via
`workbench.action.chat.open` with a `prompt` argument.