docs: add BrewPage publish example for prompts

[kochetkov-ma]

Summary

This PR adds a BrewPage publishing prompt example to the Continue documentation, demonstrating how users can leverage BrewPage's free HTML/content hosting service directly from their IDE.

What is BrewPage? A free, privacy-respecting content hosting service (https://brewpage.app) that makes it easy to share code, notes, and documents via short URLs.

Why this example? Developers using Continue often want to share work-in-progress code or documentation quickly. This prompt automates publishing selected content to BrewPage without leaving the editor.

Docs-only change: No code modifications, pure documentation addition to the prompts deep-dive guide.

See https://brewpage.app for more details.

---

Summary by cubic

Add a "Publish to BrewPage" prompt example to the prompts deep-dive so users can publish selected content and get a short URL.

• New Features
  • Example prompt that POSTs content to https://brewpage.app/api/html and returns a short URL.
  • Includes config.yaml snippet and quick usage steps to invoke the prompt from the IDE.

^{Written for commit 6b91b73. Summary will update on new commits.}

[github-actions]

Thank you for your submission, we really appreciate it. Like many open-source projects, we ask that you sign our Contributor License Agreement before we can accept your contribution. You can sign the CLA by just posting a Pull Request Comment same as the below format.

---

I have read the CLA Document and I hereby sign the CLA

---

_{You can retrigger this bot by commenting recheck in this Pull Request. Posted by the CLA Assistant Lite bot.}

[cubic-dev-ai]

No issues found across 1 file