Create a short demo video / GIF for the README

## Overview

A short visual demo would help people understand Linthra quickly — both in the README and in Fosstodon / social posts. No code required.

## What needs to be done

- [ ] Record a **20–30 second** clip of a real build
- [ ] Show a natural flow: **Library → Now Playing → Cast or Jellyfin streaming**
- [ ] Export as a GIF and/or short video suitable for the README
- [ ] Add it to the README (and note where it can be reused for posts)

## Goal

A short, clear demo that shows what Linthra does in under half a minute.

## Notes

- **No private server URLs, account names, or personal info visible** in the recording.
- Keep it real — capture from an actual running build, not a mockup.

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_Suggested labels: `help wanted`, `documentation`, `ui-polish`_

Start with the README and a real running Linthra build. Record a 20–30 second flow from Library to Now Playing to Cast or Jellyfin streaming, ensuring no private information is visible, then export a README-suitable GIF or video and add it to the README with a note about reuse for social posts.

Written by the indexing model from the issue text.