[FEATURE] Screen sharing feature

### Preflight Checklist

- [x] I have searched [existing requests](https://github.com/anthropics/claude-code/issues?q=is%3Aissue%20label%3Aenhancement) and this feature hasn't been requested yet
- [x] This is a single feature request (not multiple features)

### Problem Statement

Please add a feature letting Claude see the screen live, similar to ChatGPT's voice mode. It'd be genuinely useful for troubleshooting and just fun for casual use like gaming together. I checked with Claude directly, and this doesn't currently exist.

### Proposed Solution

Add a real time or near real time screen sharing option, similar to ChatGPT's. I don't know exactly how ChatGPT's works, but please try to replicate it. Also, make sure it lets Claude talk during it, and that you can still talk to Claude.

### Alternative Solutions

I've tried using Claude Code to make a software that sends screenshots to the chat every few seconds, but it would fill up the chat way too fast. Also considered sending video clips every minute or so, but it still fills up the chat relatively fast, and isn't truly live, since it has a minute of delay.

### Priority

Medium - Would be very helpful

### Feature Category

Interactive mode (TUI)

### Use Case Example

1. When I have an issue and don't want to waste time taking a screenshot and sending it to Claude.
2. When I just want to play games and let Claude give me tips and compliments, like a friend looking over my shoulder.

### Additional Context

_No response_

The request names no files, tests, or entry points. Start by locating the interactive-mode/TUI implementation and any existing voice or media-related entry points; done would require a scoped design and implementation for live or near-real-time screen sharing with simultaneous Claude audio interaction.

Written by the indexing model from the issue text.