Save chat contents

[explorigin]

Validations

• [X] I believe this is a way to improve. I'll try to join the Continue Discord for questions
• [X] I'm not able to find an open issue that requests the same enhancement

Problem

I've had a good chat with my AI. I'm ready to change the subject and talk about something new but my current chat was extensive and I want to refer back to it later.

Solution

Offer a button to export the chat to a markdown file.