[FEATURE] VS Code extension: support pasting images into chat input

Problem

When I paste an image from clipboard into the VS Code extension chat, it shows "[Unsupported Image]" instead of embedding the image. Other AI coding assistants (Cursor, GitHub Copilot Chat) handle this correctly — they encode pasted images as base64 and pass them to the model.

Expected behavior

Pasting an image from clipboard should encode it (base64) and include it in the message sent to Claude. Claude API supports image inputs natively — this is purely an extension-side gap, not a model limitation.

Current behavior

Image paste results in "[Unsupported Image]" placeholder. The image data is lost before reaching the model. The only workaround is to save screenshots to files and use the Read tool with a file path.

Steps to reproduce

1. Take a screenshot (Cmd+Shift+4 on macOS)
2. Paste it into the VS Code extension chat input
3. Observe "[Unsupported Image]" instead of the actual image

Environment

• VS Code extension version: 2.1.202
• macOS 25.5.0 (darwin-arm64)

Why this matters

This is a common workflow — users screenshot errors, UI bugs, diagrams, and paste them directly into chat for analysis. Forcing users to save screenshots to files first adds unnecessary friction.