Animated demo on the README and docs home #63

Why

The README and the docs home show a static SVG of the UI. A twenty-second moving picture of apic ui --demo (run a request, run a flow, switch environment, see checks land) is the single most persuasive asset the project can have, and it doubles as the intro for the course and the thumbnail material for YouTube. docs/assets/demo.tape (a VHS script) already exists but nothing renders it.

What

• task demo-gif renders docs/assets/demo.tape with vhs to docs/assets/demo.gif (and a .webm/.mp4 for the docs site, which is smaller). Update the tape to the current key bindings and to end on the checks tab with a green flow.
• Alternatively, or additionally, extend scripts/shot to emit a frame sequence and assemble an animated SVG or WebP so the asset is generated from real output without a Docker dependency; pick one and document it in AGENTS.md.
• Place it under the hero on docs/index.md (autoplay, muted, loop, with the static SVG as the poster and fallback) and at the top of the README (GIF; GitHub does not play video).
• Keep the file under ~2 MB; note the regeneration step next to task shots in AGENTS.md.

Where

docs/assets/demo.tape, Taskfile.yml, docs/index.md, README.md, scripts/shot (if the in-tree route is taken), AGENTS.md.

Tests

A CI step that renders the tape on PRs touching internal/ui or the tape, uploading the result as an artifact (not committing it), so a broken tape is noticed.