Feature request: Export chat history as a markdown file

## Problem
Chat history is stored locally in `chrome.storage.local`, no way to export, share or back it up. If the extension is uninstalled or Chrome resets its storage, all conversation history is lost.

## Proposed Solution
Add an "Export" button next to the existing "New Chat" button in the bottom. Clicking it would download current chat history as a `.md` file, formatted like:

**You**

Explain this code snippet from the documentation.

**Gemini**

This code snippet demonstrates...

The filename would include the date, e.g. `chat-export-2026-04-13.md`.

## Scope
This initial implementation would export the transcript only, since `ChatMessage` does not currently store timestamps or tab metadata. Those could be added in a future enhancement.

## Would you like me to implement this?
I am happy to submit a PR for this if it aligns with the project's goals.