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

@@ -0,0 +1,44 @@
+---
+title: Projects — save, load, new, rebuild
+description: The app-level commands for managing projects.
+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
+```
+Give the current temporary project a permanent name. (On a project that is
+already named, `save` reports that it is already auto-saved — use `save as`.)
+
+```rdbms
+save as
+```
+Copy the current project to a new name or location and switch to it.
+
+```rdbms
+new
+```
+Close the current project and start a fresh temporary one.
+
+```rdbms
+load
+```
+Open the project picker — a list of your projects, newest first, with
+`[TEMP]` markers; you can also browse to a path.
+
+```rdbms
+rebuild
+```
+Rebuild the working database from the readable files (`project.yaml` +
+`data/`), after a confirmation. Useful if the database is ever missing or out
+of date.