The selected companion everywhere, each with a small trait; next-APK notes

- state/companion.ts: one store for the chosen companion (also in localStorage so splash/login show it).
  BrandMark (the orange «π» tile) now shows the companion's symbol (Σ Δ π ω) in its colour; screen-header
  mascots, loaders and empty/error states default to it; the assistant is «از {name} بپرس» with its face,
  colour and wording; the shop, lesson and quiz «ask» buttons name it; the active tab takes its tint.
- Traits, all client-side and light: Σ sigma keeps a running tally of correct answers in the quiz header;
  Δ delta shows a flame «×N» chip and an extra buzz for answers in a row; π pi gives a short solving tip
  after a wrong answer; ω omega throws gold confetti at the end of every island whatever the score.
  Each companion's «correct» sound is pitched differently; confetti uses its colours. Characters screen
  lists each trait.
- android/README.md: what MainActivity.kt has that the installed APK lacks (vibrate bridge, media gesture,
  in-app gateway + paysInApp), what to check on a phone after building, signing owner, Bazaar policy note.

Checked in headless Chrome with Sigma, Delta and Omega selected (home, assistant, shop, characters, quiz).

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

src/components/BrandMark.tsx

@@ -1,20 +1,28 @@
+import { useId } from 'react';
+import { useCompanion } from '@/state/companion';
+
 /**
- * نشانِ تدریسینو: یک کاشیِ گرد با «π» و جرقه‌ی کوچکِ چشمک‌زن، کنارِ نامِ تدریسینو.
- * خودِ SVG است (بی‌فایلِ تصویر)، پس در هر اندازه تیز است و چیزی دانلود نمی‌شود.
+ * نشانِ تدریسینو: یک کاشیِ گرد با نمادِ همراهِ انتخابیِ کاربر (Σ، Δ، π، ω) به رنگِ همان همراه، و جرقه‌ی کوچکِ
+ * چشمک‌زن، کنارِ نامِ تدریسینو. پیش‌تر همیشه «π»ِ نارنجی بود و با همراهِ کاربر جور نبود (خواستِ مالک، ۱۴۰۵-۰۷).
+ * خودِ SVG است (بی‌فایلِ تصویر).
  */
 export function BrandMark({ size = 28, tone = 'light', withName = true }: { size?: number; tone?: 'light' | 'dark'; withName?: boolean }) {
   const ink = tone === 'light' ? '#fff' : '#3C3F8F';
+  const c = useCompanion();
+  const gid = useId();
   return (
     <span className="inline-flex items-center gap-1.5" aria-label="تدریسینو">
       <svg width={size} height={size} viewBox="0 0 32 32" aria-hidden="true">
         <defs>
-          <linearGradient id="bm-g" x1="0" y1="0" x2="1" y2="1">
-            <stop offset="0" stopColor="#FF9A5C" />
-            <stop offset="1" stopColor="#ED6956" />
+          <linearGradient id={gid} x1="0" y1="0" x2="1" y2="1">
+            <stop offset="0" stopColor={c.light} />
+            <stop offset="1" stopColor={c.color} />
           </linearGradient>
         </defs>
-        <rect x="1" y="1" width="30" height="30" rx="9" fill="url(#bm-g)" stroke={tone === 'light' ? 'rgba(255,255,255,.55)' : 'none'} />
-        <path d="M9 11.5h14M12.5 11.5v10M19 11.5v8.2c0 1.2.7 1.8 1.8 1.8" stroke="#fff" strokeWidth="2.6" strokeLinecap="round" fill="none" />
+        <rect x="1" y="1" width="30" height="30" rx="9" fill={`url(#${gid})`} stroke={tone === 'light' ? 'rgba(255,255,255,.55)' : 'none'} />
+        <text x="16" y="17" textAnchor="middle" dominantBaseline="central" fill="#fff" fontSize="19" fontWeight="900" fontFamily="Vazirmatn, system-ui, sans-serif">
+          {c.symbol}
+        </text>
         <path className="spark" d="M25 4.5l.9 1.9 1.9.9-1.9.9-.9 1.9-.9-1.9-1.9-.9 1.9-.9z" fill="#FFD23F" />
       </svg>
       {withName && <span className="font-black tracking-tight" style={{ color: ink, fontSize: size * 0.62 }}>تدریسینو</span>}