[FEATURE] Tab completion 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

I would really like to switch from Cursor to Claude Code for VS Code, but the only thing missing (being a deal breaker) would be inline tab completions.

Proposed Solution

Implement inline tab completions just like Cursor have done for the VS Code Claude Code extension.

Alternative Solutions

_No response_

Priority

Critical - Blocking my work

Feature Category

CLI commands and flags

Use Case Example

_No response_

Additional Context

_No response_