Build standalone MelodyMuse SPA

Drop the Supabase backend and call the AI provider directly from the
browser. The endpoint URL, API key, and model name are stored in
localStorage and used for direct /chat/completions requests.

- src/lib/llm.ts: config persistence, direct fetch, JSON extraction,
  shape validation, connection test
- src/lib/prompts.ts: full + partial-regeneration system prompts and
  user-message builder
- src/lib/{api,supabase}.ts removed
- supabase/ directory removed
- @supabase/supabase-js dropped from package.json
- README updated to describe the standalone architecture and CORS caveats
- .gitignore: drop Supabase entries, exclude *.tsbuildinfo

src/components/EqualizerIcon.tsx

@@ -0,0 +1,37 @@
+// Animated equalizer/waveform icon for the MelodyMuse header.
+export function EqualizerIcon({ className = 'w-7 h-7' }: { className?: string }) {
+  return (
+    <svg
+      className={className}
+      viewBox="0 0 32 32"
+      fill="none"
+      xmlns="http://www.w3.org/2000/svg"
+      aria-hidden="true"
+    >
+      <defs>
+        <linearGradient id="eq-grad" x1="0" y1="0" x2="32" y2="32" gradientUnits="userSpaceOnUse">
+          <stop offset="0" stopColor="#a78bfa" />
+          <stop offset="1" stopColor="#22d3ee" />
+        </linearGradient>
+      </defs>
+      <g stroke="url(#eq-grad)" strokeWidth="2.4" strokeLinecap="round">
+        <line x1="5" y1="13" x2="5" y2="19">
+          <animate attributeName="y1" values="13;8;13" dur="1.2s" repeatCount="indefinite" />
+          <animate attributeName="y2" values="19;24;19" dur="1.2s" repeatCount="indefinite" />
+        </line>
+        <line x1="11" y1="9" x2="11" y2="23">
+          <animate attributeName="y1" values="9;14;9" dur="1.4s" repeatCount="indefinite" />
+          <animate attributeName="y2" values="23;18;23" dur="1.4s" repeatCount="indefinite" />
+        </line>
+        <line x1="17" y1="11" x2="17" y2="21">
+          <animate attributeName="y1" values="11;6;11" dur="1.0s" repeatCount="indefinite" />
+          <animate attributeName="y2" values="21;26;21" dur="1.0s" repeatCount="indefinite" />
+        </line>
+        <line x1="23" y1="8" x2="23" y2="24">
+          <animate attributeName="y1" values="8;13;8" dur="1.6s" repeatCount="indefinite" />
+          <animate attributeName="y2" values="24;19;24" dur="1.6s" repeatCount="indefinite" />
+        </line>
+      </g>
+    </svg>
+  );
+}