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/state/askStore.ts

@@ -1,5 +1,5 @@
 import { useSyncExternalStore } from 'react';
-import type { UsedChunk } from '@/api';
+import type { Diagram, UsedChunk } from '@/api';
 import { KEYS, store } from '@/lib/storage';
 
 /**
@@ -13,6 +13,8 @@ export interface ChatMessage {
   messageId?: string;
   usedChunks?: UsedChunk[];
   followUps?: string[];
+  /** شکلِ پاسخ؛ اپ آن را خودش به SVG تبدیل می‌کند (components/Diagram). */
+  diagram?: Diagram | null;
   feedback?: 'up' | 'down';
   /** پیامِ خطا به‌جای پاسخ؛ با «دوباره» همان سوال دوباره فرستاده می‌شود. */
   failedQuestion?: string;