feat(website): projects cast (vi-nav load picker) + --demo on all casts

- New projects cast: create → save as library → new (fresh) → load → navigate
  the picker to the saved project (j, now possible via #24 vi-nav) → Enter
  loads it, the table is restored. Runs under an isolated --data-dir so the
  picker lists only this cast's projects.
- Turn on the demonstration overlay (--demo, #22 / ADR-0047) for ALL casts,
  for a consistent viewer experience: special keys show a badge — e.g.
  [ENTER], and [TAB] at the assistive-editor's completion moment, finally
  making that keystroke visible. Plain j/k navigation stays unbadged, so the
  picker navigation is not surfaced.
- Generator: per-cast `dataDir` (isolated data root) + default-on `--demo`
  (opt out with demo:false). All 7 casts regenerated.

Convert projects.md → .mdx and embed. Build clean (26 pages). Visual playback
of all casts pending a tunnel check.

website/src/content/docs/using-the-playground/projects.mdx

@@ -5,11 +5,15 @@ sidebar:
   order: 4
 ---
 
+import Demo from '../../../components/Demo.astro';
+
 A project is where your work lives. The playground saves it continuously as
 you go (see [Projects and storage](/concepts/projects-and-storage/) for the
 model), so these commands are about *switching* and *managing* projects, not
 a manual "save your changes" step.
 
+<Demo src="/casts/projects.cast" title="Save the current work as a named project, start fresh, then load it back." />
+
 ```rdbms
 save
 ```