feat(ui): new equalizer logo, favicon link, fix favicon path

- icon.svg / icon-192/512.png: blue→purple equalizer gradient design
- nginx.conf: add /app/ alias so reverse-proxy prefix resolves assets
- vite.config.js: base /app/ + %BASE_URL% in favicon links so path
  resolves correctly whether app is served at / or /app/
- ic_launcher.xml: same equalizer design for Android app icon

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

vite.config.js

@@ -1,6 +1,7 @@
 import { defineConfig } from 'vite';
 
 export default defineConfig({
+  base: '/app/',
   build: {
     outDir: 'dist',
     assetsDir: 'assets',