Add Publish to dochost to Productivity - #76

Adds Publish to dochost to Productivity.

When ChatGPT or Claude writes you an HTML page or a Markdown document, it is stuck in the chat as code. The extension adds a publish action in the chat UI that turns it into a shareable link, so you can send the rendered page to someone who is not in the conversation.

Also on the Edge Add-ons store, if the list ever wants an Edge column.

Guidelines checklist

• Searched previous suggestions — no existing dochost entry in this list
• Meaningful pull request description
• Single commit for this one suggestion
• Format [APPLICATION](LINK) - DESCRIPTION.
• Description is short and ends with a full stop
• Spelling and grammar checked
• No trailing whitespace, and npx awesome-lint reports nothing on the added line

Disclosure: I built this extension.