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/casts-src/casts.mjs

@@ -19,6 +19,28 @@
 
 /** The shared library narrative, trimmed per cast. */
 export const casts = [
+  {
+    name: 'projects',
+    title: 'Save a project, start fresh, then load it back',
+    width: 90,
+    height: 26,
+    typeSpeed: '45ms',
+    dataDir: true, // isolated data root → picker lists only this cast's projects
+    steps: [
+      { wait: 1000 },
+      { type: 'create table books with pk', after: 600 },
+      { type: 'add column to books: title (text)', after: 700 },
+      { type: "insert into books (title) values ('A Wizard of Earthsea')", after: 700 },
+      { type: 'show data books', after: 1500 }, // a saved project with content
+      { type: 'save as', after: 900 }, // opens the name prompt
+      { type: 'library', enter: true, after: 1500 }, // name it → saved as "library"
+      { type: 'new', after: 1500 }, // start fresh — the table is gone
+      { type: 'load', after: 1200 }, // opens the project picker
+      { type: 'j', enter: false, after: 1000 }, // move the selection to "library"
+      { key: 'Enter', after: 2000 }, // load it — the table is back
+      { key: 'CtrlC' }, // quit invisibly (Ctrl-C) — cast ends on the last content frame
+    ],
+  },
   {
     name: 'modes',
     title: 'Simple mode, then advanced — with the SQL the playground runs for you',