play whole islands, make home the path itself, draw tutor diagrams, add tedi

- Home is now the island path of every unit with one clear Start button on the
  current island; the six-card dashboard is gone.
- Start opens /nodes/{id}/quiz (4 questions) instead of one-question lessons, so
  an island takes one round instead of ~11. Lessons stay one tap away in the sheet.
- Tutor answers render the backend's validated diagram (plane, number line,
  fraction) as React SVG; function expressions go through a small parser, no eval.
- Tedi, the mobile-preview mascot, joins as the fourth companion with all six moods
  and an onboarding slide.
- Light polish: 3D buttons, header gradients, warmer page background.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>

src/styles/index.css

@@ -23,9 +23,9 @@
   --color-body: #3a3a5c;       /* متنِ بدنه */
   --color-muted: #9e9ec0;      /* متنِ کم‌رنگ */
   --color-faint: #b0b0c8;
-  --color-line: #ede9ff;       /* حاشیه‌ی کارت */
+  --color-line: #e9e6f7;       /* حاشیه‌ی کارت */
   --color-soft: #f0eeff;       /* پس‌زمینه‌ی ملایم */
-  --color-page: #f0f4ff;       /* پس‌زمینه‌ی صفحه */
+  --color-page: #f6f5fb;       /* پس‌زمینه‌ی صفحه؛ کمی گرم‌تر از آبیِ قبلی */
 }
 
 @layer base {